{"id":1836,"date":"2020-06-04T17:02:52","date_gmt":"2020-06-04T17:02:52","guid":{"rendered":"https:\/\/opentextbc.ca\/businesstechnicalmath\/chapter\/9-5-loans-mortgages\/"},"modified":"2022-06-15T15:37:10","modified_gmt":"2022-06-15T15:37:10","slug":"9-5-loans-mortgages","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/businesstechnicalmath\/chapter\/9-5-loans-mortgages\/","title":{"raw":"9.5 Loans and Mortgages","rendered":"9.5 Loans and Mortgages"},"content":{"raw":"<img class=\"aligncenter wp-image-1833 \" title=\"https:\/\/www.publicdomainpictures.net\/en\/view-image.php?image=112964&amp;picture=house-for-sale-sign\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2020\/06\/9.5-imagehousesale-1024x929.jpg\" alt=\"\" width=\"415\" height=\"376\" \/>\r\n<div class=\"textbox textbox--learning-objectives\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Learning Objectives<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nBy the end of this section it is expected that you will be able to:\r\n<ul>\r\n \t<li>Determine the periodic payments on an installment loan<\/li>\r\n \t<li>Determine the amount financed and the finance charge on an installment loan<\/li>\r\n \t<li>Determine the payments and finance charge on a mortgage<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<h1><strong>Installment Loans<\/strong><\/h1>\r\nA loan is something that is borrowed. In the case where this is a sum of money the amount that will be paid by the borrower will\u00a0 include the original amount plus interest.\r\n\r\nSome loans require full payment\u00a0 on the <strong>maturity date<\/strong> of the loan.\u00a0 The maturity date is when all principal and\/or interest must be repaid to the the lender. Consider a one year loan of $1000\u00a0 at a simple interest rate of 5%. At the end of one year (the maturity date) the borrower will pay back the original $1000 plus the interest of $50 for a total of $1050.\r\n\r\nFor major purchases such as vehicles or furniture there is a different type of loan, called the <strong>installment\u00a0loan<\/strong>. The average consumer cannot afford to pay $25000 or more for a new vehicle and they\u00a0 may not want to wait three or four years until they have saved enough money to do so. The qualifying consumer has the option of paying for the item with an <strong>installment loan.<\/strong>\r\n\r\nInstallment loans do not require full repayment of the loan on a specific date. With an installment loan the borrower is required to make regular (installment) payments until the loan is paid off. Each <strong>installment payment<\/strong> will include an interest charge. An installment loan can vary in length from a few years to perhaps twenty years or more (in the case of real estate).\r\n\r\nConsider an installment loan for a $4000 television. The purchaser takes out a $4000 loan with a four-year term at an interest rate of 4.5%. The monthly installment payments will be $91.21. Although the television has a purchase price of $4000, the total cost to the purchaser will be more than $4000. The total of the installment payments will be:\r\n\r\n<strong>Total Installment Payments<\/strong>\u00a0= Number of Installment Payments x Payment Amount =\r\n<p style=\"text-align: center;\">4 years x 12 payments\/year x $91.21\/mth\u00a0 = $4378.08<\/p>\r\nThe $4000 television ends up costing $4378.08 because the consumer is charged interest. Each payment includes an\u00a0interest component that adds to the overall cost of the item. The total of the interest charges is referred to as the <strong>finance charge<\/strong> on the loan.\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Finance Charge<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nThe <strong>finance charge<\/strong> is the sum of the interest charges on a loan. These interest charges are embedded in the installment payments. To calculate the finance charge:\r\n<p style=\"text-align: center;\">Finance Charge = Total Installment Payments - Loan Amount<\/p>\r\n<p style=\"text-align: center;\">= (Number of Installment Payments x Payment Amount) - Loan Amount<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\nFor the $4000 television the finance charge will be calculated as follows:\r\n<p style=\"text-align: center;\"><strong>Finance charge<\/strong> = Total Installment Payments - Loan Amount =<\/p>\r\n<p style=\"text-align: center;\">(4 years x 12 payments\/year x $91.21\/payment) - $4000 = $4378.08 - $4000 = $378.08<\/p>\r\nOver the 4-year term of the loan the purchaser will have paid the $4000 loan amount plus an additional $378.08 in interest (the finance charge).\r\n\r\nSometimes the borrower will make an <strong>initial payment<\/strong> at the time of purchase. This is called a <strong>down payment<\/strong>. When a down payment is made the remaining amount is the <strong>amount financed <\/strong>or the<strong>\u00a0 loan amount.<\/strong>\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Amount Financed<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nThe <strong>amount financed<\/strong> or <strong>loan amount<\/strong> is the purchase price of the item less any down payment:\r\n<p style=\"text-align: center;\">Amount Financed = Purchase Price - Down Payment<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\nConsider the $4000 television. Assume the purchaser makes a down payment of $1500.\r\n<p style=\"text-align: center;\">The <strong>amount financed<\/strong> is:\u00a0 Purchase Price - Down Payment = $4000 - $1500 = $2500.<\/p>\r\nIn this case the purchaser borrows $2500 rather than $4000. The amount financed is therefore $2500. Assuming the same 4-year term and an interest rate of 4.5%, the installment payments on the $2500 will be reduced to $57.01 per month. In this case the finance charge will be calculated as follows:\r\n\r\n<strong>Finance charge<\/strong> = Total Installment Payments - Loan Amount =\r\n<p style=\"text-align: center;\">(4 years x 12 payments\/year x $57.01\/payment) - $2500 = $2736.48 - $2500 = $236.48<\/p>\r\nWith the down payment of $2500 the total finance charges will be reduced to $236.48 from $378.08.\r\n\r\nThe total cost of the television to the purchaser will be:\r\n<p style=\"text-align: center;\"><strong>Purchase Price + Finance Charge <\/strong><\/p>\r\n<p style=\"text-align: center;\"><strong>= <\/strong>$4000 + $236.48 = $4236.48<\/p>\r\nAlternatively we can calculate:\r\n<p style=\"text-align: center;\"><strong>Total\u00a0 Installment Payment + Down Payment<\/strong><\/p>\r\n<p style=\"text-align: center;\">= $2736.48 + $1500 = $4236.48<\/p>\r\nAs one can see, the finance charges are a hidden but added cost. This cost will become more pronounced with more expensive purchases such as with real estate.\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Installment Loan Terminology<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n<strong>Total Installment Payments<\/strong>\u00a0= Number of payments x Payment Amount\r\n\r\n<strong>Finance Charge<\/strong> = Total Installment Payments - Loan Amount\r\n\r\n<strong>Amount Financed<\/strong> or <strong>Loan Amount<\/strong> = Purchase Price of Item\u00a0 - Down payment\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nPaul purchased a home entertainment system at a total cost of $6000. He obtained a 3 year loan at an interest rate of\u00a0 7.5%.\u00a0 His monthly payments will be $186.64 over three years.\r\n\r\na) State the amount financed.\r\n\r\nb) Determine the total installment payments.\r\n\r\nc) Determine the finance charge.\r\n\r\n<strong>Solution<\/strong>\r\n\r\na)\u00a0 Since there was no down payment the amount financed (or loan amount) will be $6000.\r\n\r\nb)\u00a0 The total installment payments will be:\r\n\r\nNumber of payments x Payment Amount\r\n\r\n= 3 years x 12 payments\/year x $186.64\r\n\r\n= $6719.04\r\n\r\nc)\u00a0 Finance Charge = Total installment payments - Loan Amount\r\n\r\n=\u00a0 $6719.04\u00a0- $6000\r\n\r\n= $719.04\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nCassie purchased a new washer and dryer at a total cost of $3800. She obtained a 4 year loan at an interest rate of\u00a0 6.2%.\u00a0 Her monthly payments will be $89.59 over four years.\r\n\r\na) State the amount financed.\r\n\r\nb) Determine the the total installment payments.\r\n\r\nc) Determine the finance charge.\r\n\r\n<details><summary>Show answer<\/summary>a)\u00a0 $3800.00\u00a0 \u00a0 b)\u00a0 $4300.32\u00a0 \u00a0 c) $500.32\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nMike purchased a home entertainment system at a total cost of $6000. He made a down payment of $1800 and to pay the balance he obtained a 3 year loan at an interest rate of\u00a0 7.5%.\u00a0 His monthly payments will be $130.65 over three years.\r\n\r\na) State the amount financed.\r\n\r\nb) Determine the total installment payments.\r\n\r\nc) Determine the finance charge.\r\n\r\nd)\u00a0 Determine the total amount that Mike paid for the home entertainment system\r\n\r\n<strong>Solution<\/strong>\r\n\r\na)\u00a0 Amount Financed = Cost of Item - Down Payment\r\n\r\n=\u00a0 $6000 - $1800 = $4200\r\n\r\nb)\u00a0 The total installment payments will be:\r\n\r\nNumber of payments x Payment Amount = 3 years x 12 payments\/year x $130.65\r\n\r\n= $4703.40\r\n\r\nc)\u00a0 Finance Charge = Total installment payments - Loan Amount\r\n\r\n=\u00a0 $4703.40 - $4200\r\n\r\n= $503.40\r\n\r\nd) Total paid = Purchase Price + Finance Charge = $6000 + $503.40 = $6503.40\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nCarl purchased a new washer and dryer at a total cost of $3800. He made a down payment of $1500 and obtained a 2 year loan for the remaining amount at an interest rate of\u00a0 6.2%.\u00a0 His monthly payments will be $102.14 over two years.\r\n\r\na) State the amount financed.\r\n\r\nb) Determine the\u00a0total installment payments.\r\n\r\nc) Determine the finance charge.\r\n\r\nd) \u00a0 Determine the total amount that Carl paid for the washer and dryer.\r\n\r\n<details><summary>Show answer<\/summary>a) $2300.00\u00a0 \u00a0b) $2451.36\r\n\r\nc)\u00a0 $151.36\u00a0 \u00a0 d)\u00a0 $3951.36\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<h1><strong>Loan Payments<\/strong><\/h1>\r\n<div data-dobid=\"dfn\">When consumers obtain installment loans they often just trust the lender to determine the installment (periodic)\u00a0 loan payments. In Example1 Paul purchased a home entertainment system at a total cost of $6000.\u00a0 He obtained a three\u00a0 year loan at an interest rate of\u00a0 7.5%. If Paul attempts to calculate his monthly payment by simply dividing the loan amount by the number of payments he will underestimate his monthly payment as he has ignored the interest component:<\/div>\r\n<div style=\"text-align: center;\" data-dobid=\"dfn\">$6000 \u00f7 36 = $166.67<\/div>\r\n<div data-dobid=\"dfn\">Paul's actual monthly payment of $186.64 <span style=\"font-size: 14pt;\">is slightly higher than Paul's estimate because of\u00a0 the interest component.<\/span><\/div>\r\n<div data-dobid=\"dfn\">The actual amount of a periodic loan payment can be determined using a formula, a table or technology. In this section we will illustrate the use of a formula.<\/div>\r\n<div data-dobid=\"dfn\">\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Periodic Payment on a Loan<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nThe <strong>periodic payment on a loan formula<\/strong> is:\r\n<p style=\"text-align: center;\">[latex] P = \\frac{A(\\frac{r}{n})}{1 - (1 + \\frac{r}{n})^{-nt}}[\/latex]<\/p>\r\n\r\n<table style=\"border-collapse: collapse; width: 100%; height: 70px;\" border=\"0\">\r\n<tbody>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"width: 33.3333%; height: 15px; text-align: center;\">P = periodic payment amount<\/td>\r\n<\/tr>\r\n<tr style=\"height: 13px;\">\r\n<td style=\"width: 33.3333%; height: 13px; text-align: center;\">A = amount of loan<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 33.3333%; height: 14px; text-align: center;\">r = annual interest rate (in decimal form)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 33.3333%; height: 14px; text-align: center;\">n = number of payments made in one year<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 33.3333%; height: 14px; text-align: center;\">t = time (in years)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 3<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nRefer back to the purchase of a television for $4000. The purchaser agrees to a 4 year term at an interest rate of 4.5%.\u00a0 \u00a0a) Use the formula to determine the monthly installment payment\u00a0 b) Determine the total installment\u00a0 payments\r\n\r\n<strong>Solution<\/strong>\r\n\r\na)\r\n\r\n[latex]P = \\frac{A(\\frac{r}{n})}{1 - (1 + \\frac{r}{n})^{-nt}}[\/latex]\r\n\r\nwhere P = payment (unknown), A = $4000, r = 4.5%, n = 12, t = 4 years\r\n<p style=\"text-align: center;\">[latex]P = \\frac{4000(\\frac{0.045}{12})}{1 - (1 + \\frac{0.045}{12})^{-12(4)}} = \\frac{15}{1-(1.00375)^{-48}} = \\frac{15}{0.16445} = 91.21[\/latex]<\/p>\r\n&nbsp;\r\n\r\nThe monthly payment is confirmed to be $91.21.\r\n\r\nb) Total installment payments =\u00a0 monthly payment amount x no. of payments\r\n\r\n$91.21 x 48= $4378.08\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT\u00a0 3<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nA dining room table set is purchased for $5600. The purchase is financed\u00a0 with a 3 year loan at an interest rate of 12.5%. a) Use the formula to determine the monthly installment payment\u00a0 b) Determine the total installment\u00a0 payments.\r\n\r\n<details open=\"open\"><summary>Show answer<\/summary>Monthly payment is $187.34; Total Installment payments [latex] =$187.34 \\times 36 = $6744.24[\/latex]\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nPaul purchased a home entertainment system at a total cost of $6000. He obtained a 3 year loan at an interest rate of\u00a0 7.5%.\u00a0 Use the formula to determine his monthly payments. Confirm that this matches the amount in Example 1.\r\n\r\n<strong>Solution<\/strong>\r\n<table style=\"border-collapse: collapse; width: 100%; height: 45px;\" border=\"0\">\r\n<tbody>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"width: 48.7466%; height: 45px;\" rowspan=\"3\">\r\n<p style=\"width: 100%;\">[latex]P = \\frac{A(\\frac{r}{n})}{1 - (1 + \\frac{r}{n})^{-nt}}[\/latex]<\/p>\r\n<\/td>\r\n<td style=\"width: 17.92%; height: 15px;\"><\/td>\r\n<td style=\"width: 33.3333%; height: 15px;\">P = payment (unknown)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"width: 17.92%; height: 15px;\">where<\/td>\r\n<td style=\"width: 33.3333%; height: 15px;\">A = $6000\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 r = 7.5%<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"width: 17.92%; height: 15px;\"><\/td>\r\n<td style=\"width: 33.3333%; height: 15px;\">n = 12\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0t = 3 years<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p style=\"text-align: center;\">[latex]P = \\frac{6000(\\frac{0.075}{12})}{1 - (1 + \\frac{0.075}{12})^{-12(3)}} = \\frac{37.5}{1-(1.00625)^{-36}} = \\frac{37.5}{0.20092} = $186.64[\/latex]<\/p>\r\n&nbsp;\r\n\r\nThe monthly payment is confirmed to be $186.64\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 4<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nCassie purchased a new washer and dryer at a total cost of $3800. She obtained a 4 year loan at an interest rate of\u00a0 6.2%.\u00a0 Use the formula to determine her monthly payments. Confirm that this matches the amount in Try It 1.\r\n\r\n<details open=\"open\"><summary>Show answer<\/summary>Monthly payment of $89.59 is confirmed\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nDetermine\u00a0 \u00a0a) the annual payments\u00a0 \u00a0b)the total installment payments\u00a0 and\u00a0 c) the finance charge on a 5 year loan of $5000 where payments are made annually and the interest rate is 6%.\r\n\r\n<strong>Solution<\/strong>\r\n\r\na)\r\n<p style=\"text-align: center;\">[latex]P = \\frac{A(\\frac{r}{n})}{1 - (1 + \\frac{r}{n})^{-nt}}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">P = payment<\/p>\r\n<p style=\"text-align: center;\">A = $5000\u00a0 \u00a0 r = 6%<\/p>\r\n<p style=\"text-align: center;\">\u00a0 \u00a0 \u00a0 \u00a0n = 1\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 t = 5 years<\/p>\r\n<p style=\"text-align: center;\">[latex]P = \\frac{5000(\\frac{0.06}{1})}{1 - (1 + \\frac{0.06}{1})^{-1(5)}} = \\frac{300}{1 - (1.06)^{-5}} = \\frac{300}{0.25274} = \\$1186.98[\/latex]<\/p>\r\nThe annual payment will be $1186.98.\r\n\r\nb) Total\u00a0 installment payments = $1186.98 x 5 = $5934.90\r\n\r\nc) Finance charge = $5934.90 - $5000 = $934.90\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 5<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nDetermine a) the annual payments\u00a0 \u00a0b) the\u00a0 total installment payments\u00a0 and\u00a0 c) the finance charge\u00a0 on a 5 year loan of $5000 where payments are made monthly and the interest rate is 6%.\r\n\r\n<details open=\"open\"><summary>Show answer<\/summary>a) Annual payment is $96.67\r\n\r\nb) Total Installment payments = $5800.20\r\n\r\nc) Finance charge $800.20\r\n\r\n<\/details><\/div>\r\n<\/div>\r\nRecall that interest is calculated only on the loan amount and not on any downpayment. When determining the periodic payment on an installment loan be sure to exclude the downpayment when\u00a0 calculating the periodic payment.\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nMike purchased a home entertainment system at a total cost of $6000. He made a down payment of $1800 and to pay the balance he obtained a 3 year loan at an interest rate of\u00a0 7.5%.\u00a0 \u00a0Use the formula to determine his monthly payments. Confirm that this matches the amount provided in Example 2.\r\n\r\n<strong>Solution<\/strong>\r\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 48.7466%;\" rowspan=\"3\">\r\n<p style=\"width: 100%;\">[latex]P = \\frac{A(\\frac{r}{n})}{1 - (1 + \\frac{r}{n})^{-nt}}[\/latex]<\/p>\r\n<\/td>\r\n<td style=\"width: 17.92%;\"><\/td>\r\n<td style=\"width: 33.3333%;\">P = payment (unknown)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 17.92%;\">where<\/td>\r\n<td style=\"width: 33.3333%;\">A = $4200\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 r = 7.5%<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 17.92%;\"><\/td>\r\n<td style=\"width: 33.3333%;\">n = 12\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0t = 3 years<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p style=\"text-align: center;\">[latex]P = \\frac{4200(\\frac{0.075}{12})}{1 - (1 + \\frac{0.075}{12})^{-12(3)}} = \\frac{26.25}{1-(1.00625)^{-36}} = \\frac{26.25}{0.20092} = $130.65[\/latex]<\/p>\r\n&nbsp;\r\n\r\nThe monthly payment is confirmed to be $130.65\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 6<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nCarl purchased a new washer and dryer at a total cost of $3800. He made a down payment of $1500 and obtained a 2 year loan for the remaining amount at an interest rate of\u00a0 6.2%.\u00a0 Use the formula to determine his monthly payments. Confirm that this matches the amount provided in Try It 2.\r\n\r\n<details open=\"open\"><summary>Show answer<\/summary>Monthly payment of $102.14 is confirmed\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 7<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nPat has decided to purchase a used vehicle that costs $12,500. He considers two options. For each option, determine a) the monthly payment\u00a0 b) total installment payments\u00a0 c) the finance charge for each option.\u00a0What is the difference in the finance charge with the down payment?\r\n\r\nOption 1) Paying the full amount with a 4 year loan, monthly payments, and an interest rate of 6.8%.\r\n\r\nOption 2) He will cancel a planned trip and and instead make a\u00a0 $3500 down payment on the purchase. He will pay the remaining amount with a 4 year loan, monthly payments, and an interest rate of 6.8%.\r\n\r\n<strong>Solution<\/strong>\r\n\r\n<span style=\"text-decoration: underline;\">Option 1)<\/span>\r\n\r\na) P = unknown\u00a0 \u00a0 \u00a0 A = $12,500\r\n\r\nr = 0.068\u00a0 \u00a0 \u00a0 \u00a0 n = 12\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 t = 4\r\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50%;\">[latex]P = \\frac{12500(\\frac{0.068}{12})}{1 - (1 + \\frac{0.068}{12})^{-(12)(4)}}[\/latex]<\/td>\r\n<td style=\"width: 50%;\">[latex] = \\frac{70.8333}{1-(1.005667)^{-48}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%;\"><\/td>\r\n<td style=\"width: 50%;\">[latex] = \\frac{70.8333}{1 - 0.76244}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%;\"><\/td>\r\n<td style=\"width: 50%;\">[latex] = \\frac{70.8333}{0.23756}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%;\"><\/td>\r\n<td style=\"width: 50%;\">[latex] = \\$298.17[\/latex] payment<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nb) Total Installment payments [latex]= \\$298.17 \\times 4 \\times 12 = \\$14,312.16[\/latex]\r\n\r\nc) Finance charge = Total Installment Payments - Loan Amount = $14312.16 - $12,500 = $1812.16\r\n\r\n<span style=\"text-decoration: underline;\">Option 2)<\/span>\r\n\r\na) P = unknown\u00a0 \u00a0 \u00a0 A = $12,500 - $3500 =$9000\r\n\r\nr = 0.068\u00a0 \u00a0 \u00a0 \u00a0 n = 12\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 t = 4\r\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50%;\">[latex]P = \\frac{9000(\\frac{0.068}{12})}{1 - (1 + \\frac{0.068}{12})^{-(12)(4)}}[\/latex]<\/td>\r\n<td style=\"width: 50%;\">[latex] = \\frac{51}{1-(1.005667)^{-48}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%;\"><\/td>\r\n<td style=\"width: 50%;\">[latex] = \\frac{51}{0.23756}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%;\"><\/td>\r\n<td style=\"width: 50%;\">[latex] = \\$214.68[\/latex] payment<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nb) Total Installment payments [latex]= (\\$214.68 \\times 4 \\times 12) = \\$10,304.64[\/latex]\r\n\r\nc) Finance charge = Total Installment Payments - Loan Amount = $10,304.64\u00a0 - $9000 = $1304.64\r\n\r\nWith a down payment there will be a savings of <strong>$507.52<\/strong> on the finance charges.\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 7<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nMick has decided to purchase a home entertainment system at a cost of\u00a0 $9200. He considers two options. For each option determine a) the monthly payment\u00a0 b) total installment payments c) the finance charge for each option. What is the difference in the finance charge with the down payment?\r\n\r\n1) Paying the full amount with a 3 year loan that offers an interest rate of 8.4%.\r\n\r\n2) Forgoing the purchase of a new electric\u00a0 bike and instead makinga $2000 down payment on the bike purchase. He will pay the remaining amount with a 3 year loan at an interest rate of 8.4%.\r\n\r\n<details><summary>Show answer<\/summary>With no down payment: a) $290\u00a0 \u00a0b)\u00a0 $10440\u00a0 \u00a0c) $1239.83\r\n\r\nWith a down payment\u00a0 a) $226.95\u00a0 b)\u00a0 \u00a0$10170.20\u00a0 \u00a0c) $970.30;\u00a0\u00a0With the down payment the finance charge is $269.53 less\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<h1><strong>Amortization\u00a0<\/strong><\/h1>\r\n<\/div>\r\n<div>Amortization\u00a0 is the process of spreading out a loan into a series of fixed payments. A portion of each payment will be applied to the interest charge and a portion will be applied to the principal amount of the loan. Although each payment is equal, the amount that applies to the interest versus the prinipal will change with each payment period. We can get a better sense of\u00a0 the impact that a loan payment has by examining the amortization schedule for a loan.<\/div>\r\n<div><\/div>\r\n<div>Consider the amortization table for the installment loan in Example 5. Recall that the loan amount is $5000 at 6% for 5 years and annual payments are $1186.98. Note then that for each year the sum of the interest and principal is equivalent to the payment of $1186.98. Refer to <a href=\"#figure1\">Figure 1<\/a> for the amortization schedule of this loan.<a id=\"figure1\"><\/a><\/div>\r\n<div><\/div>\r\n\r\n[caption id=\"attachment_1834\" align=\"aligncenter\" width=\"1024\"]<img class=\"wp-image-1834 size-large\" title=\"adapted from https:\/\/www.calculator.net\/loan-calculator.html\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/9.5-ex-1-amort-sched-1-1024x224.png\" alt=\"\" width=\"1024\" height=\"224\" \/> Fig. 1[\/caption]\r\n\r\n<div>To calculate the interest (I) we use the simple interest formula I = P<em>rt . <\/em>The principal (P) will be the beginning balance for each year. The time in years is the portion of the year for which interest is being calculated. In this example the time (t) is one year and the interest rate is 6%.<\/div>\r\n<div><\/div>\r\n<div>\r\n<div>In <strong>Year 1<\/strong> the interest on the loan of $5000 will be:<\/div>\r\n<div style=\"text-align: center;\">\u00a0 I = Prt = $5000 x 0.06 x 1yr = $300.<\/div>\r\n<div>The periodic payment amount is $1186.98 and the portion that will go towards interest is $300.<\/div>\r\n<div>The portion that will go towards paying down the principal will be:<\/div>\r\n<div style=\"text-align: center;\">periodic payment amount - interest =<\/div>\r\n<div style=\"text-align: center;\">$1186.98 - $300\u00a0 = $886.98.<\/div>\r\n<div>Although the payment was $1186.98, only $886.98 will be applied to the outstanding loan amount. At the end of year 1 the remaining balance on the loan will be:<\/div>\r\n<div style=\"text-align: center;\">beginnining balance - portion applied to the principal<\/div>\r\n<div style=\"text-align: center;\">\u00a0=\u00a0 $5000 - $886.98 = $4113.02<\/div>\r\n<div><\/div>\r\n<div><span style=\"text-align: initial; font-size: 14pt;\">In<\/span><strong style=\"text-align: initial; font-size: 14pt;\"> Year 2<\/strong><span style=\"text-align: initial; font-size: 14pt;\"> the beginning balance on the loan is $4113.02. The interest on the loan will be:<\/span><\/div>\r\n<div style=\"text-align: center;\"><span style=\"text-align: initial; font-size: 14pt;\">\u00a0 I = Prt = $4113.02 x 0.06 x 1yr = $246.78. <\/span><\/div>\r\n<div><span style=\"text-align: initial; font-size: 14pt;\">Note that interest is calculated on the remaining balance of the loan, not on the original $5000. For the periodic <\/span><span style=\"font-size: 14pt;\">payment of $1186.98, the portion that will go towards interest is $246.78.<\/span><\/div>\r\n<div>\r\n<div>The portion that will go towards paying down the principal will be:<\/div>\r\n<div style=\"text-align: center;\">periodic payment amount - interest<\/div>\r\n<div style=\"text-align: center;\">= $1186.98 - $246.78\u00a0 = $940.20.<\/div>\r\n<div>At the end of year 2 the remaining balance on the loan will be:<\/div>\r\n<div style=\"text-align: center;\">beginnining balance - portion applied to the principal<\/div>\r\n<div style=\"text-align: center;\">=\u00a0 $4113.02 - $940.20 = $3172.82<\/div>\r\n<\/div>\r\n<div>\r\n<div><\/div>\r\n<div><span style=\"text-align: initial; font-size: 14pt;\">In<\/span><strong style=\"text-align: initial; font-size: 14pt;\"> Year 3<\/strong><span style=\"text-align: initial; font-size: 14pt;\"> the beginning balance on the loan is $3172.82. The interest on the loan will be:<\/span><\/div>\r\n<div style=\"text-align: center;\"><span style=\"text-align: initial; font-size: 14pt;\">\u00a0 I = Prt = $3172.82 x 0.06 x 1yr = $190.37<\/span><\/div>\r\n<div>\r\n<div>The portion that will go towards paying down the principal will be:<\/div>\r\n<div style=\"text-align: center;\">periodic payment amount - interest<\/div>\r\n<div style=\"text-align: center;\">= $1186.98 - $190.37\u00a0 = $996.61<\/div>\r\n<div>At the end of year 3 the remaining balance on the loan will be:<\/div>\r\n<div style=\"text-align: center;\">beginnining balance - portion applied to the principal<\/div>\r\n<div style=\"text-align: center;\">= $3172.82 - $996.61 = $2176.21<\/div>\r\n<\/div>\r\n<\/div>\r\n<div>\r\n\r\nThe cycle repeats for five years until the loan is paid off. If we add the interest charges in the table they will total to $934.91. This is the same as the finance charge (ignoring the 1\u00a2 difference due to rounding) that was calculated in Example 5.\r\n\r\n<\/div>\r\n<div><\/div>\r\n<\/div>\r\n<div>The amortization table illustrates that in the early periods of the loan a larger portion of the payment goes towards interest and a smaller portion contributes to paying down the principal (loan) amount. Over time a larger portion of the payment will be applied towards paying down the balance on the loan. For large purchases it can take several payment periods before the payment contributes substantailly to the principal balance of the loan. A down payment is beneficial as it will reduce the total finance charge.<\/div>\r\n<div>\r\n<h1><strong>Mortgages<\/strong><\/h1>\r\nA long term loan that is used for the purchase of a house is called a <strong>mortgage.<\/strong> It is called a mortgage because the lending agency requires that the house be used as <strong>collateral<\/strong> for the loan. This means that if the mortgage holder is unable to make the payments the lender can take possession of the house.\r\n\r\nMortgages generally tend to be for longer time periods than an installment loan and the terms of the mortgage will often change over the course of the mortgage. Take for example the purchase of a house with a twenty year mortgage. The purchaser might sign a mortgage agreement for a five year term. The mortgage agreement will include the interest rate, the frequency of payments\u00a0 and additional rules which may allow the mortgage holder to make lump sum payments or change the payment amount. At the end of the five year term a new agreement will be required and the conditions of the mortgage usually change.\r\n\r\nAlthough it is possible to do the calculations manually, that is beyond the scope of this book. We will use technology to calculate the periodic payments and interest charges and to generate an amortization schedule.\r\n\r\nExample 8 will illustrate that amortizing a mortgage is similar to amortizing other loans except that the mortgage amortization generally involves many more payment periods.\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 8<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nA $400,000 home is purchased with a 20% down payment on a 20-year mortgage at a fixed interest rate of 3.4%.\r\n\r\na) Determine the down payment.\r\n\r\nb) Use an online mortgage calculator to determine the monthly payment and the total interest paid.\r\n\r\nc) Generate an <strong>annual<\/strong> amortization schedule.\r\n\r\nd) Determine the total payments for one\u00a0 year\r\n\r\ne) Use the table to determine how much of the first year's\u00a0 payments will go towards interest and how much will go towards the principal.\r\n\r\nf) Use the table to determine how much of the final year's\u00a0 payments will go towards interest and how much will go towards\u00a0 the principal.\r\n\r\n<strong>Solution:<\/strong>\r\n\r\na) The down payment will be 20% x $400,000 = $80,000.\r\n\r\nb)\u00a0The monthly payment will be $1839.47 and the total interest will be\u00a0 $121, 472.75.\r\n\r\nc)\r\n\r\n<img class=\"alignnone wp-image-1835 size-large\" title=\"adapted from https:\/\/www.calculator.net\/loan-calculator.html\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/9.5-ex-7-amort-sched-1024x855.png\" alt=\"\" width=\"1024\" height=\"855\" \/>\r\n\r\nd) In one year the total payments will be 12 x $1839.47 = $22,073.64.\r\n\r\ne) Of the first year's payments, almost half, $10,703.92, will go towards\u00a0 interest. $11,369.72 will go towards paying down the principal.\r\n\r\nf) Of the final year's payments, $401.22 will go towards\u00a0 interest. $21, 672.42\u00a0 will go towards the principal.\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 8<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nA 20-year mortgage is obtained to purchase a $550,000 home with a 15% down payment at a fixed interest rate of 4.6%.\r\n\r\na) Determine the down payment.\r\n\r\nb) Use an online mortgage calculator to determine the monthly payment and the total interest paid.\r\n\r\nc) Generate an <strong>annual<\/strong> amortization schedule.\r\n\r\nd) Determine the total payments for one\u00a0 year\r\n\r\ne) Use the table to determine how much of the first year's\u00a0 payments will go towards interest and how much will go towards the principal.\r\n\r\nf) Use the table to determine how much of the final year's\u00a0 payments will go towards interest and how much will go towards the principal.\r\n\r\n<details open=\"open\"><summary>Show answer<\/summary>a) The down payment will be $82,500\r\n\r\nb) the monthly payment will be $2982.93 and the total interest will be $248,403.36\r\n\r\nd) In the first year the total payments will be $35,795.16.\r\n\r\ne) In the first year $21,199.84, will go to interest. $14,595.32 will go towards paying down the principal.\r\n\r\nf) In the final year $876.17 will go to interest. $34,918.99 will go towards paying down the principal.\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 9<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nA young couple have received an inheritance and they now have enough money for\u00a0 a down payment on their first home. They plan to take out a 25 year mortgage at an interest rate of 3.8%. They are considering a new house for\u00a0 $750,000\u00a0 or a smaller older home for $380,000. If they purchase the larger house they\u00a0 plan to make a 20% down payment. With the less expensive smaller house they can afford a 35% down payment.\r\n\r\na) Use an online mortgage calculator to determine the down payment, the monthly payment and the total interest paid for each of the two houses.\r\n\r\nb) For each of the houses, what is the principal balance owing after 5 years?\r\n\r\n<strong>Solution<\/strong>\r\n\r\na) $750,000 house:\u00a0 \u00a0$150,000 down payment;\u00a0 $3101.14 monthly payment;\u00a0 Total interest $330,341.81\r\n\r\n$380,000 house:\u00a0 \u00a0$133,000 down payment;\u00a0 $1276.64 monthly payment;\u00a0 Total interest $135,990.71\r\n\r\nb)\u00a0 $750,000 house: After 5 years the balance owing is $520,767.80\r\n\r\n$380, 000 house:\u00a0 After 5 years the balance owing is $214,382.74\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 9<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nA\u00a0 couple has won $50,000 in the lottery and they decide to put this towards the purchase of a vacation cottage or a house. They plan to make a 10%\u00a0 down payment and are considering a 25 year mortgage at a rate of 2.9%. They are deciding between the purchase of a\u00a0 cottage for\u00a0 $500,000 or a house for $880,000.\r\n\r\na) Use an online mortgage calculator to determine the down payment, the monthly payment and the total interest paid for the cottage and for the house.\r\n\r\nb) For each of the cottage and the house, what is the principal balance owing after 5 years?\r\n\r\n<details open=\"open\"><summary>Show answer<\/summary>a) Cottage: The down payment will be $50,000, the monthly payment will be $2110.62 and the total interest will be $183,185.76\r\n\r\nHouse: The down payment will be $88,000, the monthly payment will be $3714.69 and the total interest will be $322,406.93\r\n\r\nb)\u00a0 Cottage: After 5 years the balance owing is $384,024.74\r\n\r\nHouse:\u00a0 After 5 years the balance owing is $675,883.55\r\n\r\n<\/details>&nbsp;\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<h1>Key Concepts<\/h1>\r\n<ul>\r\n \t<li>For an Installment Loan:\r\n<ul>\r\n \t<li>to determine the <strong>total installment payments<\/strong>:\r\n<p style=\"text-align: center;\">Number of Payments x Payment Amount<\/p>\r\n<\/li>\r\n \t<li>to determine the <strong>finance (interest) charge<\/strong>:\r\n<p style=\"text-align: center;\">\u00a0Total Installment Payments\u00a0 - Loan Amount<\/p>\r\n<\/li>\r\n \t<li>to determine the <strong>amount financed:<\/strong><\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<p style=\"text-align: center; padding-left: 40px;\">\u00a0Purchase Price - Down Payment<\/p>\r\n\r\n<ul>\r\n \t<li style=\"list-style-type: none;\">\r\n<ul>\r\n \t<li>to determine the <strong>total amount paid <\/strong>for the item:<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<p style=\"text-align: center; padding-left: 40px;\">Purchase Price + Finance Charge<\/p>\r\n<p style=\"text-align: center; padding-left: 40px;\">or<\/p>\r\n<p style=\"text-align: center; padding-left: 40px;\">Total\u00a0 Installment Payments + Down Payment<\/p>\r\n\r\n<ul>\r\n \t<li style=\"list-style-type: none;\">\r\n<ul>\r\n \t<li>to determine the <strong>periodic payment P:<\/strong><\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<p style=\"text-align: center;\">[latex] P = \\frac{A(\\frac{r}{n})}{1 - (1 + \\frac{r}{n})^{-nt}}[\/latex]<\/p>\r\n\r\n<h1><strong>Glossary<\/strong><\/h1>\r\n<div class=\"textbox shaded\">\r\n\r\n<strong>amortization<\/strong>\r\n\r\nis the process of spreading out a loan into a series of fixed payments.\r\n\r\n<strong>amount financed<\/strong>\r\n\r\nis the purchase price of the item less any down payment.\r\n\r\n<strong>finance charge<\/strong>\r\n\r\nis the total of the\u00a0 interest charges on a loan.\r\n\r\n<strong>installment loan<\/strong>\r\n\r\nis a type of loan that is repaid over time with a set number of scheduled payments (installments). The term of loan may be vary and could be few months or many years.\r\n\r\n<strong>maturity date<\/strong>\r\n\r\nis when all principal and\/or interest must be repaid to the lender.\r\n\r\n<\/div>\r\n<h1>9.5 Exercise Set<\/h1>\r\n<div>\r\n<ol>\r\n \t<li>Bette purchased a new appliance package at a total cost of $7500. She obtained a 3 year loan at an interest rate of\u00a0 5.75%.\u00a0 Her monthly payments will be $227.32 over three years.\r\n<ol type=\"a\">\r\n \t<li>State the amount financed.<\/li>\r\n \t<li>Determine the total installment payments.<\/li>\r\n \t<li>Determine the finance charge.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Paul purchased a new vehicle at a total cost of $21,300. He obtained a 5 year loan at an interest rate of\u00a0 4.2%.\u00a0 His monthly payments will be $394.20 over five years.\r\n<ol type=\"a\">\r\n \t<li>State the amount financed.<\/li>\r\n \t<li>Determine the total installment payments.<\/li>\r\n \t<li>Determine the finance charge.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Theresa purchased a home entertainment system at a total cost of $4300. She made a down payment of $1000 and to pay the balance she obtained a 2 year loan at an interest rate of\u00a0 5.5%.\u00a0 Her monthly payments will be $145.52 over two years.\r\n<ol type=\"a\">\r\n \t<li>State the amount financed.<\/li>\r\n \t<li>Determine the total installment payments.<\/li>\r\n \t<li>Determine the finance charge.<\/li>\r\n \t<li>Determine the total amount that Theresa paid for the home entertainment system.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>The Johnsons purchased a new vehicle at a total cost of $32,500. They made a down payment of $5000 and to pay the balance they obtained a 4 year loan at an interest rate of\u00a0 3.6%.\u00a0 The monthly payments will be $616.01 over four years.\r\n<ol type=\"a\">\r\n \t<li>State the amount financed.<\/li>\r\n \t<li>Determine the total installment payments..<\/li>\r\n \t<li>Determine the finance charge.<\/li>\r\n \t<li>Determine the total amount that the Johnsons paid for the vehicle.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Determine the monthly (periodic) payment and finance charge for each of the following installment loans.\r\n<table class=\"grid\" style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 20%; text-align: center;\">Annual Interest Rate<\/td>\r\n<td style=\"width: 20%; text-align: center;\">Number of Years<\/td>\r\n<td style=\"width: 20%; text-align: center;\">Loan Amount<\/td>\r\n<td style=\"width: 20%; text-align: center;\">Monthly Payment<\/td>\r\n<td style=\"width: 20%; text-align: center;\">Finance Charge<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 20%; text-align: center;\">2.8%<\/td>\r\n<td style=\"width: 20%; text-align: center;\">1<\/td>\r\n<td style=\"width: 20%; text-align: center;\">$2000<\/td>\r\n<td style=\"width: 20%; text-align: center;\"><\/td>\r\n<td style=\"width: 20%; text-align: center;\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 20%; text-align: center;\">4%<\/td>\r\n<td style=\"width: 20%; text-align: center;\">2<\/td>\r\n<td style=\"width: 20%; text-align: center;\">$4200<\/td>\r\n<td style=\"width: 20%; text-align: center;\"><\/td>\r\n<td style=\"width: 20%; text-align: center;\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 20%; text-align: center;\">5%<\/td>\r\n<td style=\"width: 20%; text-align: center;\">3<\/td>\r\n<td style=\"width: 20%; text-align: center;\">$5200<\/td>\r\n<td style=\"width: 20%; text-align: center;\"><\/td>\r\n<td style=\"width: 20%; text-align: center;\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 20%; text-align: center;\">4.5%<\/td>\r\n<td style=\"width: 20%; text-align: center;\">3<\/td>\r\n<td style=\"width: 20%; text-align: center;\">$8000<\/td>\r\n<td style=\"width: 20%; text-align: center;\"><\/td>\r\n<td style=\"width: 20%; text-align: center;\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 20%; text-align: center;\">6.5%<\/td>\r\n<td style=\"width: 20%; text-align: center;\">4<\/td>\r\n<td style=\"width: 20%; text-align: center;\">$11,000<\/td>\r\n<td style=\"width: 20%; text-align: center;\"><\/td>\r\n<td style=\"width: 20%; text-align: center;\"><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/li>\r\n \t<li>A dining room set is purchased for $2300. The purchase is financed\u00a0 with a 2 year loan at an interest rate of 6.4%\r\n<ol type=\"a\">\r\n \t<li>Use the formula to determine the monthly payment<\/li>\r\n \t<li>Determine the total installment\u00a0 payments.<\/li>\r\n \t<li>Determine the finance charge.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>A new vehicle is purchased for $32, 000. The purchase is financed\u00a0 with a 5 year loan at an interest rate of 4.8%.\r\n<ol type=\"a\">\r\n \t<li>Use the formula to determine the monthly payment<\/li>\r\n \t<li>Determine the total installment\u00a0 payments.<\/li>\r\n \t<li>Determine the finance charge.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>The Connors purchase a hot tub for a total price of $8500. They make a downpayment of $2300 and finance the remainder with a 3 year loan at an interest rate of 2.6%.\r\n<ol type=\"a\">\r\n \t<li>Determine the loan amount<\/li>\r\n \t<li>Use the formula to determine the monthly payment<\/li>\r\n \t<li>Determine the total installment\u00a0 payments.<\/li>\r\n \t<li>Determine the finance charge.<\/li>\r\n \t<li>How much in total did the Connors actually pay for the hot tub?<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>The Tanners purchase a small RV for a total price of $48,000. They make a downpayment of $8000 and finance the remainder with a 4 year loan at an interest rate of 3%.\r\n<ol type=\"a\">\r\n \t<li>Determine the loan amount<\/li>\r\n \t<li>Use the formula to determine the monthly payment<\/li>\r\n \t<li>Determine the total installment\u00a0 payments.<\/li>\r\n \t<li>Determine the finance charge.<\/li>\r\n \t<li>How much in total did the Tanners actually pay for the RV?<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Matt borrows $4000 for 4 years at an interest rate of 5%. He will make 4 annual payments.\r\n<ol type=\"a\">\r\n \t<li>Determine the annual payment and the finance charge.<\/li>\r\n \t<li>Complete the following amortization table for the loan.\r\n<table class=\"grid\" style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 20%; text-align: center;\">Year<\/td>\r\n<td style=\"width: 17.5852%; text-align: center;\">Beginning Balance<\/td>\r\n<td style=\"width: 19.1478%; text-align: center;\">Interest<\/td>\r\n<td style=\"width: 23.267%; text-align: center;\">Payment towards the Principal\r\n\r\n= Payment - Interest<\/td>\r\n<td style=\"width: 20%; text-align: center;\">End Balance<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 20%; text-align: center;\">1<\/td>\r\n<td style=\"width: 17.5852%; text-align: center;\">$4000<\/td>\r\n<td style=\"width: 19.1478%; text-align: center;\">$200<\/td>\r\n<td style=\"width: 23.267%;\"><\/td>\r\n<td style=\"width: 20%;\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 20%; text-align: center;\">2<\/td>\r\n<td style=\"width: 17.5852%;\"><\/td>\r\n<td style=\"width: 19.1478%;\"><\/td>\r\n<td style=\"width: 23.267%;\"><\/td>\r\n<td style=\"width: 20%;\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 20%; text-align: center;\">3<\/td>\r\n<td style=\"width: 17.5852%;\"><\/td>\r\n<td style=\"width: 19.1478%;\"><\/td>\r\n<td style=\"width: 23.267%;\"><\/td>\r\n<td style=\"width: 20%;\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 20%; text-align: center;\">4<\/td>\r\n<td style=\"width: 17.5852%;\"><\/td>\r\n<td style=\"width: 19.1478%;\"><\/td>\r\n<td style=\"width: 23.267%;\"><\/td>\r\n<td style=\"width: 20%;\"><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/li>\r\n \t<li>Confirm the finance charge by totalling the interest column.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Kate purchases an electric bike for $4800 and she makes a down payment of $2200. She takes out a one year loan at 3.2% to pay the balance owing in monthly payments.\r\n<ol type=\"a\">\r\n \t<li>Determine the amount of the loan<\/li>\r\n \t<li>Determine the monthly payment on the loan.<\/li>\r\n \t<li>Determine the total installment payments<\/li>\r\n \t<li>Determine the finance charge.<\/li>\r\n \t<li>Complete the following amortization table for the first four months of the loan. (Hint: When calculating simple interest the time (t) will be 1\/12 of\u00a0 a year).\r\n<table class=\"grid\" style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 20%; text-align: center;\">Year<\/td>\r\n<td style=\"width: 17.5852%; text-align: center;\">Beginning Balance<\/td>\r\n<td style=\"width: 19.1478%; text-align: center;\">Interest<\/td>\r\n<td style=\"width: 23.267%; text-align: center;\">Payment towards the Principal\r\n\r\n= Payment - Interest<\/td>\r\n<td style=\"width: 20%; text-align: center;\">End Balance<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 20%; text-align: center;\">1<\/td>\r\n<td style=\"width: 17.5852%; text-align: center;\"><\/td>\r\n<td style=\"width: 19.1478%; text-align: center;\"><\/td>\r\n<td style=\"width: 23.267%;\"><\/td>\r\n<td style=\"width: 20%;\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 20%; text-align: center;\">2<\/td>\r\n<td style=\"width: 17.5852%;\"><\/td>\r\n<td style=\"width: 19.1478%;\"><\/td>\r\n<td style=\"width: 23.267%;\"><\/td>\r\n<td style=\"width: 20%;\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 20%; text-align: center;\">3<\/td>\r\n<td style=\"width: 17.5852%;\"><\/td>\r\n<td style=\"width: 19.1478%;\"><\/td>\r\n<td style=\"width: 23.267%;\"><\/td>\r\n<td style=\"width: 20%;\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 20%; text-align: center;\">4<\/td>\r\n<td style=\"width: 17.5852%;\"><\/td>\r\n<td style=\"width: 19.1478%;\"><\/td>\r\n<td style=\"width: 23.267%;\"><\/td>\r\n<td style=\"width: 20%;\"><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/li>\r\n \t<li>How much did Kate actually pay for the bike?<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>You purchase a kayak for $4800 and take out a 3 year loan with monthly payments at an annual interest rate of 3.5%. You are pondering whether to put $2000 down or go on a holiday with that $2000.\r\n<ol type=\"a\">\r\n \t<li>Assuming no down payment, determine the monthly payment, total installment payments,\u00a0 and finance charge.<\/li>\r\n \t<li>Assuming a down payment of $2000, determine the monthly payment, total installment payments,\u00a0 and finance charge.<\/li>\r\n \t<li>What is the difference in finance charges between the two options?<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Nick purchases a used motorbike for $12,000 and takes out a 4 year loan with monthly payments at an annual interest rate of 5%.\r\n<ol type=\"a\">\r\n \t<li>Determine the payment, total installment payments, and finance charge with no down payment.<\/li>\r\n \t<li>Determine the payment, total installment payments, and finance charge with a down payment of $4000.<\/li>\r\n \t<li>What is the difference in finance charges between the two options?<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>A $350,000 home is purchased with a 20 year mortgage at a fixed interest rate of 3.4% and a down payment of 10%.\r\n<ol type=\"a\">\r\n \t<li>Use an online mortgage calculator to determine the down payment, the monthly payment and the total interest paid.<\/li>\r\n \t<li>Determine the total payments for one year.<\/li>\r\n \t<li>Generate an amortization schedule and determine how much of the first year's payments will go towards principle and how much will go towards interest.<\/li>\r\n \t<li>Generate an amortization schedule and determine how much of the final year's payments will go towards principle and how much will go towards interest.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>A $350,000 home is purchased with a 20 year mortgage at a fixed interest rate of 3.4% and a\u00a0 20% down payment.\r\n<ol type=\"a\">\r\n \t<li>Use an online mortgage calculator to determine the down payment, the monthly payment and the total interest paid<\/li>\r\n \t<li>Compare your answers for #14 and #15 Part a). What was the impact on the monthly payment and the total interest charges when the down payment was doubled?<\/li>\r\n \t<li>Determine the total payments for one year.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>A $650,000 home is purchased with a 10% down payment on a 25 year mortgage at a fixed interest rate of 4.2%. \u00a0Use an online mortgage calculator to determine the down payment, the monthly payment and the total interest paid.<\/li>\r\n \t<li>\u00a0A $650,000 home is purchased with a 10% down payment on a 25 year mortgage at a fixed interest rate of 2.2%. \u00a0Use an online mortgage calculator to determine the down payment, the monthly payment and the total interest paid<\/li>\r\n \t<li>Compare your answers for parts a) and b). How does the lower interest rate impact the total interest paid?<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n<h1>Answers<\/h1>\r\n<ol>\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>$7500<\/li>\r\n \t<li>$8183.52<\/li>\r\n \t<li>$683.52<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>$21,300<\/li>\r\n \t<li>$23,652<\/li>\r\n \t<li>$2352<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>$3300<\/li>\r\n \t<li>$3492.48<\/li>\r\n \t<li>$192.48<\/li>\r\n \t<li>$4492.48<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>$27,500<\/li>\r\n \t<li>$29,568.48<\/li>\r\n \t<li>$2068.48<\/li>\r\n \t<li>$34,568.48<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<table class=\"grid\" style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 20%; text-align: center;\">Annual Interest Rate<\/td>\r\n<td style=\"width: 20%; text-align: center;\">Number of Years<\/td>\r\n<td style=\"width: 20%; text-align: center;\">Loan Amount<\/td>\r\n<td style=\"width: 20%; text-align: center;\">Monthly Payment<\/td>\r\n<td style=\"width: 20%; text-align: center;\">Finance Charge<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 20%; text-align: center;\">2.8%<\/td>\r\n<td style=\"width: 20%; text-align: center;\">1<\/td>\r\n<td style=\"width: 20%; text-align: center;\">$2000<\/td>\r\n<td style=\"width: 20%; text-align: center;\"><strong>$169.21<\/strong><\/td>\r\n<td style=\"width: 20%; text-align: center;\">$30.52<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 20%; text-align: center;\">4%<\/td>\r\n<td style=\"width: 20%; text-align: center;\">2<\/td>\r\n<td style=\"width: 20%; text-align: center;\">$4200<\/td>\r\n<td style=\"width: 20%; text-align: center;\"><strong>$182.38<\/strong><\/td>\r\n<td style=\"width: 20%; text-align: center;\">$177.12<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 20%; text-align: center;\">5%<\/td>\r\n<td style=\"width: 20%; text-align: center;\">3<\/td>\r\n<td style=\"width: 20%; text-align: center;\">$5200<\/td>\r\n<td style=\"width: 20%; text-align: center;\"><strong>$155.85<\/strong><\/td>\r\n<td style=\"width: 20%; text-align: center;\">$410.60<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 20%; text-align: center;\">4.5%<\/td>\r\n<td style=\"width: 20%; text-align: center;\">3<\/td>\r\n<td style=\"width: 20%; text-align: center;\">$8000<\/td>\r\n<td style=\"width: 20%; text-align: center;\"><strong>$237.98<\/strong><\/td>\r\n<td style=\"width: 20%; text-align: center;\">$567.28<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 20%; text-align: center;\">6.5%<\/td>\r\n<td style=\"width: 20%; text-align: center;\">4<\/td>\r\n<td style=\"width: 20%; text-align: center;\">$11,000<\/td>\r\n<td style=\"width: 20%; text-align: center;\"><strong>$260.86<\/strong><\/td>\r\n<td style=\"width: 20%; text-align: center;\">$1521.28<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/li>\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>$102.35<\/li>\r\n \t<li>$2456.40<\/li>\r\n \t<li>$156.40<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>$600.95<\/li>\r\n \t<li>$36,057<\/li>\r\n \t<li>$4057<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>$6200<\/li>\r\n \t<li>$179.21<\/li>\r\n \t<li>$6451.56<\/li>\r\n \t<li>$251.56<\/li>\r\n \t<li>$8751.56<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>$40,000<\/li>\r\n \t<li>$885.37<\/li>\r\n \t<li>$42,497.76<\/li>\r\n \t<li>$2497.76<\/li>\r\n \t<li>$50,497.76<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>Annual Payment = $1128.05. Finance Charge = [latex](1128.05 \\times 4) - 4000 = \\$512.20 [\/latex]<\/li>\r\n \t<li>\r\n<table class=\"grid\" style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 7.30964%; text-align: center;\">Year<\/td>\r\n<td style=\"width: 14.9239%; text-align: center;\">Beginning Balance<\/td>\r\n<td style=\"width: 14.5614%; text-align: center;\">Interest<\/td>\r\n<td style=\"width: 30.8773%; text-align: center;\">Payment towards the\u00a0 \u00a0 \u00a0 \u00a0Principal (Balance)\r\n\r\n= Payment - Interest<\/td>\r\n<td style=\"width: 32.3278%; text-align: center;\">End Balance<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 7.30964%; text-align: center;\">1<\/td>\r\n<td style=\"width: 14.9239%; text-align: center;\">4000<\/td>\r\n<td style=\"width: 14.5614%; text-align: center;\">200<\/td>\r\n<td style=\"width: 30.8773%; text-align: center;\">1128.05 - 200 = 928.05<\/td>\r\n<td style=\"width: 32.3278%; text-align: center;\">4000 - 928.05 = 3071.95<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 7.30964%; text-align: center;\">2<\/td>\r\n<td style=\"width: 14.9239%; text-align: center;\">3071.95<\/td>\r\n<td style=\"width: 14.5614%; text-align: center;\">153.60<\/td>\r\n<td style=\"width: 30.8773%; text-align: center;\">1128.05 - 153.60 = 974.45<\/td>\r\n<td style=\"width: 32.3278%; text-align: center;\">3071.95 - 974.45 = 2097.50<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 7.30964%; text-align: center;\">3<\/td>\r\n<td style=\"width: 14.9239%; text-align: center;\">2097.50<\/td>\r\n<td style=\"width: 14.5614%; text-align: center;\">104.87<\/td>\r\n<td style=\"width: 30.8773%; text-align: center;\">1128.05 - 104.87 = 1023.18<\/td>\r\n<td style=\"width: 32.3278%; text-align: center;\">2097.50 - 1023.28 = 1074.32<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 7.30964%; text-align: center;\">4<\/td>\r\n<td style=\"width: 14.9239%; text-align: center;\">1074.32<\/td>\r\n<td style=\"width: 14.5614%; text-align: center;\">53.72<\/td>\r\n<td style=\"width: 30.8773%; text-align: center;\">1128.05 - 53.72 = 1074.33<\/td>\r\n<td style=\"width: 32.3278%; text-align: center;\">1074.32 - 1074.33 = 0<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/li>\r\n \t<li>Interest = $512.19 (rounding difference of 1\u00a2)<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>Loan Amount = $2600<\/li>\r\n \t<li>Monthly Payment = $220.44<\/li>\r\n \t<li>Total Installment payments = $2645.28<\/li>\r\n \t<li>Finance Charge =\u00a0 $45.28<\/li>\r\n \t<li>\r\n<table class=\"grid\" style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 7.30964%; text-align: center;\">Year<\/td>\r\n<td style=\"width: 14.9239%; text-align: center;\">Beginning Balance<\/td>\r\n<td style=\"width: 14.5614%; text-align: center;\">Interest\r\n\r\n(t = 1\/12 year)<\/td>\r\n<td style=\"width: 30.8773%; text-align: center;\">Payment towards the\u00a0 \u00a0 \u00a0 \u00a0Principal (Balance)\r\n\r\n= Payment - Interest<\/td>\r\n<td style=\"width: 32.3278%; text-align: center;\">End Balance<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 7.30964%; text-align: center;\">1<\/td>\r\n<td style=\"width: 14.9239%; text-align: center;\">2600<\/td>\r\n<td style=\"width: 14.5614%; text-align: center;\">6.93<\/td>\r\n<td style=\"width: 30.8773%; text-align: center;\">220.44 - 6.93 = 213.51<\/td>\r\n<td style=\"width: 32.3278%; text-align: center;\">2600 - 213.51 = 2386.49<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 7.30964%; text-align: center;\">2<\/td>\r\n<td style=\"width: 14.9239%; text-align: center;\">2386.49<\/td>\r\n<td style=\"width: 14.5614%; text-align: center;\">6.36<\/td>\r\n<td style=\"width: 30.8773%; text-align: center;\">220.44 - 6.36 = 214.08<\/td>\r\n<td style=\"width: 32.3278%; text-align: center;\">2386.49 - 214.08 = 2172.41<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 7.30964%; text-align: center;\">3<\/td>\r\n<td style=\"width: 14.9239%; text-align: center;\">2172.41<\/td>\r\n<td style=\"width: 14.5614%; text-align: center;\">5.79<\/td>\r\n<td style=\"width: 30.8773%; text-align: center;\">220.44 - 5.79 = 214.65<\/td>\r\n<td style=\"width: 32.3278%; text-align: center;\">2172.41 - 214.65 = 1957.76<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 7.30964%; text-align: center;\">4<\/td>\r\n<td style=\"width: 14.9239%; text-align: center;\">1957.76<\/td>\r\n<td style=\"width: 14.5614%; text-align: center;\">5.22<\/td>\r\n<td style=\"width: 30.8773%; text-align: center;\">220.44 - 5.22 = 215.22<\/td>\r\n<td style=\"width: 32.3278%; text-align: center;\">1957.76 - 215.22 = 1742.54<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/li>\r\n \t<li>$4845.28<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>Payment = $140.65;\u00a0 \u00a0Total Installment Payments = $5063.40;\u00a0 Finance Charge = $263.40<\/li>\r\n \t<li>Payment = $82.05;\u00a0 \u00a0Total Installment Payments = $2953.65 Finance Charge = $153.65<\/li>\r\n \t<li>$109.75 less with a down payment<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>Payment = $276.35;\u00a0 Total\u00a0 Installment Payments = $13264.80;\u00a0 Finance Charge = $1264.80<\/li>\r\n \t<li>Payment = $184.23;\u00a0 Total Installment Payments = $8843.04;\u00a0 Finance Charge = $843.04<\/li>\r\n \t<li>$421.76 less with a down payment<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>down payment of $35,000; monthly payment of $1810.73;\u00a0 total interest paid\u00a0 $119,574.74<\/li>\r\n \t<li>total payments for one year $21,728.76<\/li>\r\n \t<li>$10,536.66 towards interest and $11,192.10 towards principal.<\/li>\r\n \t<li>$394.95 towards interest and $21,333.81 towards principal.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>down payment of $70,000; monthly payment of $1609.54;\u00a0 total interest paid\u00a0 $106,288.66<\/li>\r\n \t<li>With the downpayment being doubled, the monthly payment was reduced by close to $200 and the total interest paid was reduced by more than $13,000.<\/li>\r\n \t<li>$19,314.48<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>down payment of $65,000; monthly payment of $3152.81;\u00a0 total interest paid\u00a0 $360,843.77<\/li>\r\n \t<li>down payment of $65,000; monthly payment of $2536.90;\u00a0 total interest paid\u00a0 $176,070.84<\/li>\r\n \t<li>the total interest is almost $200,000 less!<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n<\/div>","rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1833\" title=\"https:\/\/www.publicdomainpictures.net\/en\/view-image.php?image=112964&amp;picture=house-for-sale-sign\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2020\/06\/9.5-imagehousesale-1024x929.jpg\" alt=\"\" width=\"415\" height=\"376\" srcset=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/uploads\/sites\/361\/2020\/06\/9.5-imagehousesale-1024x929.jpg 1024w, https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/uploads\/sites\/361\/2020\/06\/9.5-imagehousesale-300x272.jpg 300w, https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/uploads\/sites\/361\/2020\/06\/9.5-imagehousesale-768x697.jpg 768w, https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/uploads\/sites\/361\/2020\/06\/9.5-imagehousesale-1536x1394.jpg 1536w, https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/uploads\/sites\/361\/2020\/06\/9.5-imagehousesale-65x59.jpg 65w, https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/uploads\/sites\/361\/2020\/06\/9.5-imagehousesale-225x204.jpg 225w, https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/uploads\/sites\/361\/2020\/06\/9.5-imagehousesale-350x318.jpg 350w, https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/uploads\/sites\/361\/2020\/06\/9.5-imagehousesale.jpg 1920w\" sizes=\"auto, (max-width: 415px) 100vw, 415px\" \/><\/p>\n<div class=\"textbox textbox--learning-objectives\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Objectives<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>By the end of this section it is expected that you will be able to:<\/p>\n<ul>\n<li>Determine the periodic payments on an installment loan<\/li>\n<li>Determine the amount financed and the finance charge on an installment loan<\/li>\n<li>Determine the payments and finance charge on a mortgage<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1><strong>Installment Loans<\/strong><\/h1>\n<p>A loan is something that is borrowed. In the case where this is a sum of money the amount that will be paid by the borrower will\u00a0 include the original amount plus interest.<\/p>\n<p>Some loans require full payment\u00a0 on the <strong>maturity date<\/strong> of the loan.\u00a0 The maturity date is when all principal and\/or interest must be repaid to the the lender. Consider a one year loan of $1000\u00a0 at a simple interest rate of 5%. At the end of one year (the maturity date) the borrower will pay back the original $1000 plus the interest of $50 for a total of $1050.<\/p>\n<p>For major purchases such as vehicles or furniture there is a different type of loan, called the <strong>installment\u00a0loan<\/strong>. The average consumer cannot afford to pay $25000 or more for a new vehicle and they\u00a0 may not want to wait three or four years until they have saved enough money to do so. The qualifying consumer has the option of paying for the item with an <strong>installment loan.<\/strong><\/p>\n<p>Installment loans do not require full repayment of the loan on a specific date. With an installment loan the borrower is required to make regular (installment) payments until the loan is paid off. Each <strong>installment payment<\/strong> will include an interest charge. An installment loan can vary in length from a few years to perhaps twenty years or more (in the case of real estate).<\/p>\n<p>Consider an installment loan for a $4000 television. The purchaser takes out a $4000 loan with a four-year term at an interest rate of 4.5%. The monthly installment payments will be $91.21. Although the television has a purchase price of $4000, the total cost to the purchaser will be more than $4000. The total of the installment payments will be:<\/p>\n<p><strong>Total Installment Payments<\/strong>\u00a0= Number of Installment Payments x Payment Amount =<\/p>\n<p style=\"text-align: center;\">4 years x 12 payments\/year x $91.21\/mth\u00a0 = $4378.08<\/p>\n<p>The $4000 television ends up costing $4378.08 because the consumer is charged interest. Each payment includes an\u00a0interest component that adds to the overall cost of the item. The total of the interest charges is referred to as the <strong>finance charge<\/strong> on the loan.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Finance Charge<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>The <strong>finance charge<\/strong> is the sum of the interest charges on a loan. These interest charges are embedded in the installment payments. To calculate the finance charge:<\/p>\n<p style=\"text-align: center;\">Finance Charge = Total Installment Payments &#8211; Loan Amount<\/p>\n<p style=\"text-align: center;\">= (Number of Installment Payments x Payment Amount) &#8211; Loan Amount<\/p>\n<\/div>\n<\/div>\n<p>For the $4000 television the finance charge will be calculated as follows:<\/p>\n<p style=\"text-align: center;\"><strong>Finance charge<\/strong> = Total Installment Payments &#8211; Loan Amount =<\/p>\n<p style=\"text-align: center;\">(4 years x 12 payments\/year x $91.21\/payment) &#8211; $4000 = $4378.08 &#8211; $4000 = $378.08<\/p>\n<p>Over the 4-year term of the loan the purchaser will have paid the $4000 loan amount plus an additional $378.08 in interest (the finance charge).<\/p>\n<p>Sometimes the borrower will make an <strong>initial payment<\/strong> at the time of purchase. This is called a <strong>down payment<\/strong>. When a down payment is made the remaining amount is the <strong>amount financed <\/strong>or the<strong>\u00a0 loan amount.<\/strong><\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Amount Financed<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>The <strong>amount financed<\/strong> or <strong>loan amount<\/strong> is the purchase price of the item less any down payment:<\/p>\n<p style=\"text-align: center;\">Amount Financed = Purchase Price &#8211; Down Payment<\/p>\n<\/div>\n<\/div>\n<p>Consider the $4000 television. Assume the purchaser makes a down payment of $1500.<\/p>\n<p style=\"text-align: center;\">The <strong>amount financed<\/strong> is:\u00a0 Purchase Price &#8211; Down Payment = $4000 &#8211; $1500 = $2500.<\/p>\n<p>In this case the purchaser borrows $2500 rather than $4000. The amount financed is therefore $2500. Assuming the same 4-year term and an interest rate of 4.5%, the installment payments on the $2500 will be reduced to $57.01 per month. In this case the finance charge will be calculated as follows:<\/p>\n<p><strong>Finance charge<\/strong> = Total Installment Payments &#8211; Loan Amount =<\/p>\n<p style=\"text-align: center;\">(4 years x 12 payments\/year x $57.01\/payment) &#8211; $2500 = $2736.48 &#8211; $2500 = $236.48<\/p>\n<p>With the down payment of $2500 the total finance charges will be reduced to $236.48 from $378.08.<\/p>\n<p>The total cost of the television to the purchaser will be:<\/p>\n<p style=\"text-align: center;\"><strong>Purchase Price + Finance Charge <\/strong><\/p>\n<p style=\"text-align: center;\"><strong>= <\/strong>$4000 + $236.48 = $4236.48<\/p>\n<p>Alternatively we can calculate:<\/p>\n<p style=\"text-align: center;\"><strong>Total\u00a0 Installment Payment + Down Payment<\/strong><\/p>\n<p style=\"text-align: center;\">= $2736.48 + $1500 = $4236.48<\/p>\n<p>As one can see, the finance charges are a hidden but added cost. This cost will become more pronounced with more expensive purchases such as with real estate.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Installment Loan Terminology<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p><strong>Total Installment Payments<\/strong>\u00a0= Number of payments x Payment Amount<\/p>\n<p><strong>Finance Charge<\/strong> = Total Installment Payments &#8211; Loan Amount<\/p>\n<p><strong>Amount Financed<\/strong> or <strong>Loan Amount<\/strong> = Purchase Price of Item\u00a0 &#8211; Down payment<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Paul purchased a home entertainment system at a total cost of $6000. He obtained a 3 year loan at an interest rate of\u00a0 7.5%.\u00a0 His monthly payments will be $186.64 over three years.<\/p>\n<p>a) State the amount financed.<\/p>\n<p>b) Determine the total installment payments.<\/p>\n<p>c) Determine the finance charge.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<p>a)\u00a0 Since there was no down payment the amount financed (or loan amount) will be $6000.<\/p>\n<p>b)\u00a0 The total installment payments will be:<\/p>\n<p>Number of payments x Payment Amount<\/p>\n<p>= 3 years x 12 payments\/year x $186.64<\/p>\n<p>= $6719.04<\/p>\n<p>c)\u00a0 Finance Charge = Total installment payments &#8211; Loan Amount<\/p>\n<p>=\u00a0 $6719.04\u00a0&#8211; $6000<\/p>\n<p>= $719.04<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Cassie purchased a new washer and dryer at a total cost of $3800. She obtained a 4 year loan at an interest rate of\u00a0 6.2%.\u00a0 Her monthly payments will be $89.59 over four years.<\/p>\n<p>a) State the amount financed.<\/p>\n<p>b) Determine the the total installment payments.<\/p>\n<p>c) Determine the finance charge.<\/p>\n<details>\n<summary>Show answer<\/summary>\n<p>a)\u00a0 $3800.00\u00a0 \u00a0 b)\u00a0 $4300.32\u00a0 \u00a0 c) $500.32<\/p>\n<\/details>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Mike purchased a home entertainment system at a total cost of $6000. He made a down payment of $1800 and to pay the balance he obtained a 3 year loan at an interest rate of\u00a0 7.5%.\u00a0 His monthly payments will be $130.65 over three years.<\/p>\n<p>a) State the amount financed.<\/p>\n<p>b) Determine the total installment payments.<\/p>\n<p>c) Determine the finance charge.<\/p>\n<p>d)\u00a0 Determine the total amount that Mike paid for the home entertainment system<\/p>\n<p><strong>Solution<\/strong><\/p>\n<p>a)\u00a0 Amount Financed = Cost of Item &#8211; Down Payment<\/p>\n<p>=\u00a0 $6000 &#8211; $1800 = $4200<\/p>\n<p>b)\u00a0 The total installment payments will be:<\/p>\n<p>Number of payments x Payment Amount = 3 years x 12 payments\/year x $130.65<\/p>\n<p>= $4703.40<\/p>\n<p>c)\u00a0 Finance Charge = Total installment payments &#8211; Loan Amount<\/p>\n<p>=\u00a0 $4703.40 &#8211; $4200<\/p>\n<p>= $503.40<\/p>\n<p>d) Total paid = Purchase Price + Finance Charge = $6000 + $503.40 = $6503.40<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Carl purchased a new washer and dryer at a total cost of $3800. He made a down payment of $1500 and obtained a 2 year loan for the remaining amount at an interest rate of\u00a0 6.2%.\u00a0 His monthly payments will be $102.14 over two years.<\/p>\n<p>a) State the amount financed.<\/p>\n<p>b) Determine the\u00a0total installment payments.<\/p>\n<p>c) Determine the finance charge.<\/p>\n<p>d) \u00a0 Determine the total amount that Carl paid for the washer and dryer.<\/p>\n<details>\n<summary>Show answer<\/summary>\n<p>a) $2300.00\u00a0 \u00a0b) $2451.36<\/p>\n<p>c)\u00a0 $151.36\u00a0 \u00a0 d)\u00a0 $3951.36<\/p>\n<\/details>\n<\/div>\n<\/div>\n<h1><strong>Loan Payments<\/strong><\/h1>\n<div data-dobid=\"dfn\">When consumers obtain installment loans they often just trust the lender to determine the installment (periodic)\u00a0 loan payments. In Example1 Paul purchased a home entertainment system at a total cost of $6000.\u00a0 He obtained a three\u00a0 year loan at an interest rate of\u00a0 7.5%. If Paul attempts to calculate his monthly payment by simply dividing the loan amount by the number of payments he will underestimate his monthly payment as he has ignored the interest component:<\/div>\n<div style=\"text-align: center;\" data-dobid=\"dfn\">$6000 \u00f7 36 = $166.67<\/div>\n<div data-dobid=\"dfn\">Paul&#8217;s actual monthly payment of $186.64 <span style=\"font-size: 14pt;\">is slightly higher than Paul&#8217;s estimate because of\u00a0 the interest component.<\/span><\/div>\n<div data-dobid=\"dfn\">The actual amount of a periodic loan payment can be determined using a formula, a table or technology. In this section we will illustrate the use of a formula.<\/div>\n<div data-dobid=\"dfn\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Periodic Payment on a Loan<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>The <strong>periodic payment on a loan formula<\/strong> is:<\/p>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f48374414889122191e897c69588c538_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#80;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#65;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#114;&#125;&#123;&#110;&#125;&#41;&#125;&#123;&#49;&#32;&#45;&#32;&#40;&#49;&#32;&#43;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#114;&#125;&#123;&#110;&#125;&#41;&#94;&#123;&#45;&#110;&#116;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"119\" style=\"vertical-align: -12px;\" \/><\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 70px;\">\n<tbody>\n<tr style=\"height: 15px;\">\n<td style=\"width: 33.3333%; height: 15px; text-align: center;\">P = periodic payment amount<\/td>\n<\/tr>\n<tr style=\"height: 13px;\">\n<td style=\"width: 33.3333%; height: 13px; text-align: center;\">A = amount of loan<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 33.3333%; height: 14px; text-align: center;\">r = annual interest rate (in decimal form)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 33.3333%; height: 14px; text-align: center;\">n = number of payments made in one year<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 33.3333%; height: 14px; text-align: center;\">t = time (in years)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 3<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Refer back to the purchase of a television for $4000. The purchaser agrees to a 4 year term at an interest rate of 4.5%.\u00a0 \u00a0a) Use the formula to determine the monthly installment payment\u00a0 b) Determine the total installment\u00a0 payments<\/p>\n<p><strong>Solution<\/strong><\/p>\n<p>a)<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-820ffde4c657a9c0619f78cb1ad162ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#65;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#114;&#125;&#123;&#110;&#125;&#41;&#125;&#123;&#49;&#32;&#45;&#32;&#40;&#49;&#32;&#43;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#114;&#125;&#123;&#110;&#125;&#41;&#94;&#123;&#45;&#110;&#116;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"119\" style=\"vertical-align: -12px;\" \/><\/p>\n<p>where P = payment (unknown), A = $4000, r = 4.5%, n = 12, t = 4 years<\/p>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-90846b4ebb72e14f54802eba7c18694c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#48;&#48;&#48;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#48;&#46;&#48;&#52;&#53;&#125;&#123;&#49;&#50;&#125;&#41;&#125;&#123;&#49;&#32;&#45;&#32;&#40;&#49;&#32;&#43;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#48;&#46;&#48;&#52;&#53;&#125;&#123;&#49;&#50;&#125;&#41;&#94;&#123;&#45;&#49;&#50;&#40;&#52;&#41;&#125;&#125;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#53;&#125;&#123;&#49;&#45;&#40;&#49;&#46;&#48;&#48;&#51;&#55;&#53;&#41;&#94;&#123;&#45;&#52;&#56;&#125;&#125;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#53;&#125;&#123;&#48;&#46;&#49;&#54;&#52;&#52;&#53;&#125;&#32;&#61;&#32;&#57;&#49;&#46;&#50;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"415\" style=\"vertical-align: -13px;\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>The monthly payment is confirmed to be $91.21.<\/p>\n<p>b) Total installment payments =\u00a0 monthly payment amount x no. of payments<\/p>\n<p>$91.21 x 48= $4378.08<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT\u00a0 3<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>A dining room table set is purchased for $5600. The purchase is financed\u00a0 with a 3 year loan at an interest rate of 12.5%. a) Use the formula to determine the monthly installment payment\u00a0 b) Determine the total installment\u00a0 payments.<\/p>\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p>Monthly payment is $187.34; Total Installment payments <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c6c68b5b91d20540fb7e75a9fb859ea7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#61;&#36;&#49;&#56;&#55;&#46;&#51;&#52;&#32;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#51;&#54;&#32;&#61;&#32;&#36;&#54;&#55;&#52;&#52;&#46;&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"178\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Paul purchased a home entertainment system at a total cost of $6000. He obtained a 3 year loan at an interest rate of\u00a0 7.5%.\u00a0 Use the formula to determine his monthly payments. Confirm that this matches the amount in Example 1.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 45px;\">\n<tbody>\n<tr style=\"height: 15px;\">\n<td style=\"width: 48.7466%; height: 45px;\" rowspan=\"3\">\n<p style=\"width: 100%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-820ffde4c657a9c0619f78cb1ad162ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#65;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#114;&#125;&#123;&#110;&#125;&#41;&#125;&#123;&#49;&#32;&#45;&#32;&#40;&#49;&#32;&#43;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#114;&#125;&#123;&#110;&#125;&#41;&#94;&#123;&#45;&#110;&#116;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"119\" style=\"vertical-align: -12px;\" \/><\/p>\n<\/td>\n<td style=\"width: 17.92%; height: 15px;\"><\/td>\n<td style=\"width: 33.3333%; height: 15px;\">P = payment (unknown)<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 17.92%; height: 15px;\">where<\/td>\n<td style=\"width: 33.3333%; height: 15px;\">A = $6000\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 r = 7.5%<\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 17.92%; height: 15px;\"><\/td>\n<td style=\"width: 33.3333%; height: 15px;\">n = 12\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0t = 3 years<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8838aedb99a4961b715a47308ab02551_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#54;&#48;&#48;&#48;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#48;&#46;&#48;&#55;&#53;&#125;&#123;&#49;&#50;&#125;&#41;&#125;&#123;&#49;&#32;&#45;&#32;&#40;&#49;&#32;&#43;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#48;&#46;&#48;&#55;&#53;&#125;&#123;&#49;&#50;&#125;&#41;&#94;&#123;&#45;&#49;&#50;&#40;&#51;&#41;&#125;&#125;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#55;&#46;&#53;&#125;&#123;&#49;&#45;&#40;&#49;&#46;&#48;&#48;&#54;&#50;&#53;&#41;&#94;&#123;&#45;&#51;&#54;&#125;&#125;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#55;&#46;&#53;&#125;&#123;&#48;&#46;&#50;&#48;&#48;&#57;&#50;&#125;&#32;&#61;&#32;&#36;&#49;&#56;&#54;&#46;&#54;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"420\" style=\"vertical-align: -13px;\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>The monthly payment is confirmed to be $186.64<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Cassie purchased a new washer and dryer at a total cost of $3800. She obtained a 4 year loan at an interest rate of\u00a0 6.2%.\u00a0 Use the formula to determine her monthly payments. Confirm that this matches the amount in Try It 1.<\/p>\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p>Monthly payment of $89.59 is confirmed<\/p>\n<\/details>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Determine\u00a0 \u00a0a) the annual payments\u00a0 \u00a0b)the total installment payments\u00a0 and\u00a0 c) the finance charge on a 5 year loan of $5000 where payments are made annually and the interest rate is 6%.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<p>a)<\/p>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-820ffde4c657a9c0619f78cb1ad162ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#65;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#114;&#125;&#123;&#110;&#125;&#41;&#125;&#123;&#49;&#32;&#45;&#32;&#40;&#49;&#32;&#43;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#114;&#125;&#123;&#110;&#125;&#41;&#94;&#123;&#45;&#110;&#116;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"119\" style=\"vertical-align: -12px;\" \/><\/p>\n<p style=\"text-align: center;\">P = payment<\/p>\n<p style=\"text-align: center;\">A = $5000\u00a0 \u00a0 r = 6%<\/p>\n<p style=\"text-align: center;\">\u00a0 \u00a0 \u00a0 \u00a0n = 1\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 t = 5 years<\/p>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-cb4f41f5a5f70b1fff293da12aba90a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#48;&#48;&#48;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#48;&#46;&#48;&#54;&#125;&#123;&#49;&#125;&#41;&#125;&#123;&#49;&#32;&#45;&#32;&#40;&#49;&#32;&#43;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#48;&#46;&#48;&#54;&#125;&#123;&#49;&#125;&#41;&#94;&#123;&#45;&#49;&#40;&#53;&#41;&#125;&#125;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#48;&#48;&#125;&#123;&#49;&#32;&#45;&#32;&#40;&#49;&#46;&#48;&#54;&#41;&#94;&#123;&#45;&#53;&#125;&#125;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#48;&#48;&#125;&#123;&#48;&#46;&#50;&#53;&#50;&#55;&#52;&#125;&#32;&#61;&#32;&#92;&#36;&#49;&#49;&#56;&#54;&#46;&#57;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"405\" style=\"vertical-align: -13px;\" \/><\/p>\n<p>The annual payment will be $1186.98.<\/p>\n<p>b) Total\u00a0 installment payments = $1186.98 x 5 = $5934.90<\/p>\n<p>c) Finance charge = $5934.90 &#8211; $5000 = $934.90<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Determine a) the annual payments\u00a0 \u00a0b) the\u00a0 total installment payments\u00a0 and\u00a0 c) the finance charge\u00a0 on a 5 year loan of $5000 where payments are made monthly and the interest rate is 6%.<\/p>\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p>a) Annual payment is $96.67<\/p>\n<p>b) Total Installment payments = $5800.20<\/p>\n<p>c) Finance charge $800.20<\/p>\n<\/details>\n<\/div>\n<\/div>\n<p>Recall that interest is calculated only on the loan amount and not on any downpayment. When determining the periodic payment on an installment loan be sure to exclude the downpayment when\u00a0 calculating the periodic payment.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Mike purchased a home entertainment system at a total cost of $6000. He made a down payment of $1800 and to pay the balance he obtained a 3 year loan at an interest rate of\u00a0 7.5%.\u00a0 \u00a0Use the formula to determine his monthly payments. Confirm that this matches the amount provided in Example 2.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 48.7466%;\" rowspan=\"3\">\n<p style=\"width: 100%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-820ffde4c657a9c0619f78cb1ad162ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#65;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#114;&#125;&#123;&#110;&#125;&#41;&#125;&#123;&#49;&#32;&#45;&#32;&#40;&#49;&#32;&#43;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#114;&#125;&#123;&#110;&#125;&#41;&#94;&#123;&#45;&#110;&#116;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"119\" style=\"vertical-align: -12px;\" \/><\/p>\n<\/td>\n<td style=\"width: 17.92%;\"><\/td>\n<td style=\"width: 33.3333%;\">P = payment (unknown)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 17.92%;\">where<\/td>\n<td style=\"width: 33.3333%;\">A = $4200\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 r = 7.5%<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 17.92%;\"><\/td>\n<td style=\"width: 33.3333%;\">n = 12\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0t = 3 years<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-fd8656d742c54a5347ba75ced773aa09_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#50;&#48;&#48;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#48;&#46;&#48;&#55;&#53;&#125;&#123;&#49;&#50;&#125;&#41;&#125;&#123;&#49;&#32;&#45;&#32;&#40;&#49;&#32;&#43;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#48;&#46;&#48;&#55;&#53;&#125;&#123;&#49;&#50;&#125;&#41;&#94;&#123;&#45;&#49;&#50;&#40;&#51;&#41;&#125;&#125;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#54;&#46;&#50;&#53;&#125;&#123;&#49;&#45;&#40;&#49;&#46;&#48;&#48;&#54;&#50;&#53;&#41;&#94;&#123;&#45;&#51;&#54;&#125;&#125;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#54;&#46;&#50;&#53;&#125;&#123;&#48;&#46;&#50;&#48;&#48;&#57;&#50;&#125;&#32;&#61;&#32;&#36;&#49;&#51;&#48;&#46;&#54;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"419\" style=\"vertical-align: -13px;\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>The monthly payment is confirmed to be $130.65<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Carl purchased a new washer and dryer at a total cost of $3800. He made a down payment of $1500 and obtained a 2 year loan for the remaining amount at an interest rate of\u00a0 6.2%.\u00a0 Use the formula to determine his monthly payments. Confirm that this matches the amount provided in Try It 2.<\/p>\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p>Monthly payment of $102.14 is confirmed<\/p>\n<\/details>\n<\/div>\n<\/div>\n<div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 7<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Pat has decided to purchase a used vehicle that costs $12,500. He considers two options. For each option, determine a) the monthly payment\u00a0 b) total installment payments\u00a0 c) the finance charge for each option.\u00a0What is the difference in the finance charge with the down payment?<\/p>\n<p>Option 1) Paying the full amount with a 4 year loan, monthly payments, and an interest rate of 6.8%.<\/p>\n<p>Option 2) He will cancel a planned trip and and instead make a\u00a0 $3500 down payment on the purchase. He will pay the remaining amount with a 4 year loan, monthly payments, and an interest rate of 6.8%.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<p><span style=\"text-decoration: underline;\">Option 1)<\/span><\/p>\n<p>a) P = unknown\u00a0 \u00a0 \u00a0 A = $12,500<\/p>\n<p>r = 0.068\u00a0 \u00a0 \u00a0 \u00a0 n = 12\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 t = 4<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6b7a7d6f04b443bf74270da22c0e740f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#50;&#53;&#48;&#48;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#48;&#46;&#48;&#54;&#56;&#125;&#123;&#49;&#50;&#125;&#41;&#125;&#123;&#49;&#32;&#45;&#32;&#40;&#49;&#32;&#43;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#48;&#46;&#48;&#54;&#56;&#125;&#123;&#49;&#50;&#125;&#41;&#94;&#123;&#45;&#40;&#49;&#50;&#41;&#40;&#52;&#41;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"163\" style=\"vertical-align: -13px;\" \/><\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-877c7ce9a7db05c43f66208e3af9705a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#48;&#46;&#56;&#51;&#51;&#51;&#125;&#123;&#49;&#45;&#40;&#49;&#46;&#48;&#48;&#53;&#54;&#54;&#55;&#41;&#94;&#123;&#45;&#52;&#56;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"27\" width=\"124\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-275dd4eabcb6e31d7fc62dd217d20b1b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#48;&#46;&#56;&#51;&#51;&#51;&#125;&#123;&#49;&#32;&#45;&#32;&#48;&#46;&#55;&#54;&#50;&#52;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"84\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0c82513cd5e5ccc8b615e04f9483a2d5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#48;&#46;&#56;&#51;&#51;&#51;&#125;&#123;&#48;&#46;&#50;&#51;&#55;&#53;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"67\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b335e24b64f59e2654fc6fd896afb497_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#61;&#32;&#92;&#36;&#50;&#57;&#56;&#46;&#49;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"78\" style=\"vertical-align: -1px;\" \/> payment<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>b) Total Installment payments <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a5faa5040d0eeb853f77bcd5d35de6ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#61;&#32;&#92;&#36;&#50;&#57;&#56;&#46;&#49;&#55;&#32;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#52;&#32;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#49;&#50;&#32;&#61;&#32;&#92;&#36;&#49;&#52;&#44;&#51;&#49;&#50;&#46;&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"255\" style=\"vertical-align: -4px;\" \/><\/p>\n<p>c) Finance charge = Total Installment Payments &#8211; Loan Amount = $14312.16 &#8211; $12,500 = $1812.16<\/p>\n<p><span style=\"text-decoration: underline;\">Option 2)<\/span><\/p>\n<p>a) P = unknown\u00a0 \u00a0 \u00a0 A = $12,500 &#8211; $3500 =$9000<\/p>\n<p>r = 0.068\u00a0 \u00a0 \u00a0 \u00a0 n = 12\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 t = 4<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4ebf234ebc7040195fd6d861a5121cb1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#80;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#48;&#48;&#48;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#48;&#46;&#48;&#54;&#56;&#125;&#123;&#49;&#50;&#125;&#41;&#125;&#123;&#49;&#32;&#45;&#32;&#40;&#49;&#32;&#43;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#48;&#46;&#48;&#54;&#56;&#125;&#123;&#49;&#50;&#125;&#41;&#94;&#123;&#45;&#40;&#49;&#50;&#41;&#40;&#52;&#41;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"163\" style=\"vertical-align: -13px;\" \/><\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-71b1f16682629f1c336aeeac0e774d9d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#49;&#125;&#123;&#49;&#45;&#40;&#49;&#46;&#48;&#48;&#53;&#54;&#54;&#55;&#41;&#94;&#123;&#45;&#52;&#56;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"27\" width=\"124\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-51b1f38c5b9afabbcbfe82f27ff30ad6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#49;&#125;&#123;&#48;&#46;&#50;&#51;&#55;&#53;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"67\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><\/td>\n<td style=\"width: 50%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4a6179c41eae6a239c785db9e5552eeb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#61;&#32;&#92;&#36;&#50;&#49;&#52;&#46;&#54;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"78\" style=\"vertical-align: -1px;\" \/> payment<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>b) Total Installment payments <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-235cd9067678d1d5674b969fb8629f14_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#61;&#32;&#40;&#92;&#36;&#50;&#49;&#52;&#46;&#54;&#56;&#32;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#52;&#32;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#49;&#50;&#41;&#32;&#61;&#32;&#92;&#36;&#49;&#48;&#44;&#51;&#48;&#52;&#46;&#54;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"269\" style=\"vertical-align: -5px;\" \/><\/p>\n<p>c) Finance charge = Total Installment Payments &#8211; Loan Amount = $10,304.64\u00a0 &#8211; $9000 = $1304.64<\/p>\n<p>With a down payment there will be a savings of <strong>$507.52<\/strong> on the finance charges.<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Mick has decided to purchase a home entertainment system at a cost of\u00a0 $9200. He considers two options. For each option determine a) the monthly payment\u00a0 b) total installment payments c) the finance charge for each option. What is the difference in the finance charge with the down payment?<\/p>\n<p>1) Paying the full amount with a 3 year loan that offers an interest rate of 8.4%.<\/p>\n<p>2) Forgoing the purchase of a new electric\u00a0 bike and instead makinga $2000 down payment on the bike purchase. He will pay the remaining amount with a 3 year loan at an interest rate of 8.4%.<\/p>\n<details>\n<summary>Show answer<\/summary>\n<p>With no down payment: a) $290\u00a0 \u00a0b)\u00a0 $10440\u00a0 \u00a0c) $1239.83<\/p>\n<p>With a down payment\u00a0 a) $226.95\u00a0 b)\u00a0 \u00a0$10170.20\u00a0 \u00a0c) $970.30;\u00a0\u00a0With the down payment the finance charge is $269.53 less<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<h1><strong>Amortization\u00a0<\/strong><\/h1>\n<\/div>\n<div>Amortization\u00a0 is the process of spreading out a loan into a series of fixed payments. A portion of each payment will be applied to the interest charge and a portion will be applied to the principal amount of the loan. Although each payment is equal, the amount that applies to the interest versus the prinipal will change with each payment period. We can get a better sense of\u00a0 the impact that a loan payment has by examining the amortization schedule for a loan.<\/div>\n<div><\/div>\n<div>Consider the amortization table for the installment loan in Example 5. Recall that the loan amount is $5000 at 6% for 5 years and annual payments are $1186.98. Note then that for each year the sum of the interest and principal is equivalent to the payment of $1186.98. Refer to <a href=\"#figure1\">Figure 1<\/a> for the amortization schedule of this loan.<a id=\"figure1\"><\/a><\/div>\n<div><\/div>\n<figure id=\"attachment_1834\" aria-describedby=\"caption-attachment-1834\" style=\"width: 1024px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1834 size-large\" title=\"adapted from https:\/\/www.calculator.net\/loan-calculator.html\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/9.5-ex-1-amort-sched-1-1024x224.png\" alt=\"\" width=\"1024\" height=\"224\" srcset=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/uploads\/sites\/361\/2021\/08\/9.5-ex-1-amort-sched-1-1024x224.png 1024w, https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/uploads\/sites\/361\/2021\/08\/9.5-ex-1-amort-sched-1-300x66.png 300w, https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/uploads\/sites\/361\/2021\/08\/9.5-ex-1-amort-sched-1-768x168.png 768w, https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/uploads\/sites\/361\/2021\/08\/9.5-ex-1-amort-sched-1-65x14.png 65w, https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/uploads\/sites\/361\/2021\/08\/9.5-ex-1-amort-sched-1-225x49.png 225w, https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/uploads\/sites\/361\/2021\/08\/9.5-ex-1-amort-sched-1-350x77.png 350w, https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/uploads\/sites\/361\/2021\/08\/9.5-ex-1-amort-sched-1.png 1450w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption id=\"caption-attachment-1834\" class=\"wp-caption-text\">Fig. 1<\/figcaption><\/figure>\n<div>To calculate the interest (I) we use the simple interest formula I = P<em>rt . <\/em>The principal (P) will be the beginning balance for each year. The time in years is the portion of the year for which interest is being calculated. In this example the time (t) is one year and the interest rate is 6%.<\/div>\n<div><\/div>\n<div>\n<div>In <strong>Year 1<\/strong> the interest on the loan of $5000 will be:<\/div>\n<div style=\"text-align: center;\">\u00a0 I = Prt = $5000 x 0.06 x 1yr = $300.<\/div>\n<div>The periodic payment amount is $1186.98 and the portion that will go towards interest is $300.<\/div>\n<div>The portion that will go towards paying down the principal will be:<\/div>\n<div style=\"text-align: center;\">periodic payment amount &#8211; interest =<\/div>\n<div style=\"text-align: center;\">$1186.98 &#8211; $300\u00a0 = $886.98.<\/div>\n<div>Although the payment was $1186.98, only $886.98 will be applied to the outstanding loan amount. At the end of year 1 the remaining balance on the loan will be:<\/div>\n<div style=\"text-align: center;\">beginnining balance &#8211; portion applied to the principal<\/div>\n<div style=\"text-align: center;\">\u00a0=\u00a0 $5000 &#8211; $886.98 = $4113.02<\/div>\n<div><\/div>\n<div><span style=\"text-align: initial; font-size: 14pt;\">In<\/span><strong style=\"text-align: initial; font-size: 14pt;\"> Year 2<\/strong><span style=\"text-align: initial; font-size: 14pt;\"> the beginning balance on the loan is $4113.02. The interest on the loan will be:<\/span><\/div>\n<div style=\"text-align: center;\"><span style=\"text-align: initial; font-size: 14pt;\">\u00a0 I = Prt = $4113.02 x 0.06 x 1yr = $246.78. <\/span><\/div>\n<div><span style=\"text-align: initial; font-size: 14pt;\">Note that interest is calculated on the remaining balance of the loan, not on the original $5000. For the periodic <\/span><span style=\"font-size: 14pt;\">payment of $1186.98, the portion that will go towards interest is $246.78.<\/span><\/div>\n<div>\n<div>The portion that will go towards paying down the principal will be:<\/div>\n<div style=\"text-align: center;\">periodic payment amount &#8211; interest<\/div>\n<div style=\"text-align: center;\">= $1186.98 &#8211; $246.78\u00a0 = $940.20.<\/div>\n<div>At the end of year 2 the remaining balance on the loan will be:<\/div>\n<div style=\"text-align: center;\">beginnining balance &#8211; portion applied to the principal<\/div>\n<div style=\"text-align: center;\">=\u00a0 $4113.02 &#8211; $940.20 = $3172.82<\/div>\n<\/div>\n<div>\n<div><\/div>\n<div><span style=\"text-align: initial; font-size: 14pt;\">In<\/span><strong style=\"text-align: initial; font-size: 14pt;\"> Year 3<\/strong><span style=\"text-align: initial; font-size: 14pt;\"> the beginning balance on the loan is $3172.82. The interest on the loan will be:<\/span><\/div>\n<div style=\"text-align: center;\"><span style=\"text-align: initial; font-size: 14pt;\">\u00a0 I = Prt = $3172.82 x 0.06 x 1yr = $190.37<\/span><\/div>\n<div>\n<div>The portion that will go towards paying down the principal will be:<\/div>\n<div style=\"text-align: center;\">periodic payment amount &#8211; interest<\/div>\n<div style=\"text-align: center;\">= $1186.98 &#8211; $190.37\u00a0 = $996.61<\/div>\n<div>At the end of year 3 the remaining balance on the loan will be:<\/div>\n<div style=\"text-align: center;\">beginnining balance &#8211; portion applied to the principal<\/div>\n<div style=\"text-align: center;\">= $3172.82 &#8211; $996.61 = $2176.21<\/div>\n<\/div>\n<\/div>\n<div>\n<p>The cycle repeats for five years until the loan is paid off. If we add the interest charges in the table they will total to $934.91. This is the same as the finance charge (ignoring the 1\u00a2 difference due to rounding) that was calculated in Example 5.<\/p>\n<\/div>\n<div><\/div>\n<\/div>\n<div>The amortization table illustrates that in the early periods of the loan a larger portion of the payment goes towards interest and a smaller portion contributes to paying down the principal (loan) amount. Over time a larger portion of the payment will be applied towards paying down the balance on the loan. For large purchases it can take several payment periods before the payment contributes substantailly to the principal balance of the loan. A down payment is beneficial as it will reduce the total finance charge.<\/div>\n<div>\n<h1><strong>Mortgages<\/strong><\/h1>\n<p>A long term loan that is used for the purchase of a house is called a <strong>mortgage.<\/strong> It is called a mortgage because the lending agency requires that the house be used as <strong>collateral<\/strong> for the loan. This means that if the mortgage holder is unable to make the payments the lender can take possession of the house.<\/p>\n<p>Mortgages generally tend to be for longer time periods than an installment loan and the terms of the mortgage will often change over the course of the mortgage. Take for example the purchase of a house with a twenty year mortgage. The purchaser might sign a mortgage agreement for a five year term. The mortgage agreement will include the interest rate, the frequency of payments\u00a0 and additional rules which may allow the mortgage holder to make lump sum payments or change the payment amount. At the end of the five year term a new agreement will be required and the conditions of the mortgage usually change.<\/p>\n<p>Although it is possible to do the calculations manually, that is beyond the scope of this book. We will use technology to calculate the periodic payments and interest charges and to generate an amortization schedule.<\/p>\n<p>Example 8 will illustrate that amortizing a mortgage is similar to amortizing other loans except that the mortgage amortization generally involves many more payment periods.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 8<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>A $400,000 home is purchased with a 20% down payment on a 20-year mortgage at a fixed interest rate of 3.4%.<\/p>\n<p>a) Determine the down payment.<\/p>\n<p>b) Use an online mortgage calculator to determine the monthly payment and the total interest paid.<\/p>\n<p>c) Generate an <strong>annual<\/strong> amortization schedule.<\/p>\n<p>d) Determine the total payments for one\u00a0 year<\/p>\n<p>e) Use the table to determine how much of the first year&#8217;s\u00a0 payments will go towards interest and how much will go towards the principal.<\/p>\n<p>f) Use the table to determine how much of the final year&#8217;s\u00a0 payments will go towards interest and how much will go towards\u00a0 the principal.<\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>a) The down payment will be 20% x $400,000 = $80,000.<\/p>\n<p>b)\u00a0The monthly payment will be $1839.47 and the total interest will be\u00a0 $121, 472.75.<\/p>\n<p>c)<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1835 size-large\" title=\"adapted from https:\/\/www.calculator.net\/loan-calculator.html\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/9.5-ex-7-amort-sched-1024x855.png\" alt=\"\" width=\"1024\" height=\"855\" srcset=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/uploads\/sites\/361\/2021\/08\/9.5-ex-7-amort-sched-1024x855.png 1024w, https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/uploads\/sites\/361\/2021\/08\/9.5-ex-7-amort-sched-300x251.png 300w, https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/uploads\/sites\/361\/2021\/08\/9.5-ex-7-amort-sched-768x641.png 768w, https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/uploads\/sites\/361\/2021\/08\/9.5-ex-7-amort-sched-65x54.png 65w, https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/uploads\/sites\/361\/2021\/08\/9.5-ex-7-amort-sched-225x188.png 225w, https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/uploads\/sites\/361\/2021\/08\/9.5-ex-7-amort-sched-350x292.png 350w, https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/uploads\/sites\/361\/2021\/08\/9.5-ex-7-amort-sched.png 1505w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/p>\n<p>d) In one year the total payments will be 12 x $1839.47 = $22,073.64.<\/p>\n<p>e) Of the first year&#8217;s payments, almost half, $10,703.92, will go towards\u00a0 interest. $11,369.72 will go towards paying down the principal.<\/p>\n<p>f) Of the final year&#8217;s payments, $401.22 will go towards\u00a0 interest. $21, 672.42\u00a0 will go towards the principal.<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>A 20-year mortgage is obtained to purchase a $550,000 home with a 15% down payment at a fixed interest rate of 4.6%.<\/p>\n<p>a) Determine the down payment.<\/p>\n<p>b) Use an online mortgage calculator to determine the monthly payment and the total interest paid.<\/p>\n<p>c) Generate an <strong>annual<\/strong> amortization schedule.<\/p>\n<p>d) Determine the total payments for one\u00a0 year<\/p>\n<p>e) Use the table to determine how much of the first year&#8217;s\u00a0 payments will go towards interest and how much will go towards the principal.<\/p>\n<p>f) Use the table to determine how much of the final year&#8217;s\u00a0 payments will go towards interest and how much will go towards the principal.<\/p>\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p>a) The down payment will be $82,500<\/p>\n<p>b) the monthly payment will be $2982.93 and the total interest will be $248,403.36<\/p>\n<p>d) In the first year the total payments will be $35,795.16.<\/p>\n<p>e) In the first year $21,199.84, will go to interest. $14,595.32 will go towards paying down the principal.<\/p>\n<p>f) In the final year $876.17 will go to interest. $34,918.99 will go towards paying down the principal.<\/p>\n<\/details>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 9<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>A young couple have received an inheritance and they now have enough money for\u00a0 a down payment on their first home. They plan to take out a 25 year mortgage at an interest rate of 3.8%. They are considering a new house for\u00a0 $750,000\u00a0 or a smaller older home for $380,000. If they purchase the larger house they\u00a0 plan to make a 20% down payment. With the less expensive smaller house they can afford a 35% down payment.<\/p>\n<p>a) Use an online mortgage calculator to determine the down payment, the monthly payment and the total interest paid for each of the two houses.<\/p>\n<p>b) For each of the houses, what is the principal balance owing after 5 years?<\/p>\n<p><strong>Solution<\/strong><\/p>\n<p>a) $750,000 house:\u00a0 \u00a0$150,000 down payment;\u00a0 $3101.14 monthly payment;\u00a0 Total interest $330,341.81<\/p>\n<p>$380,000 house:\u00a0 \u00a0$133,000 down payment;\u00a0 $1276.64 monthly payment;\u00a0 Total interest $135,990.71<\/p>\n<p>b)\u00a0 $750,000 house: After 5 years the balance owing is $520,767.80<\/p>\n<p>$380, 000 house:\u00a0 After 5 years the balance owing is $214,382.74<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>A\u00a0 couple has won $50,000 in the lottery and they decide to put this towards the purchase of a vacation cottage or a house. They plan to make a 10%\u00a0 down payment and are considering a 25 year mortgage at a rate of 2.9%. They are deciding between the purchase of a\u00a0 cottage for\u00a0 $500,000 or a house for $880,000.<\/p>\n<p>a) Use an online mortgage calculator to determine the down payment, the monthly payment and the total interest paid for the cottage and for the house.<\/p>\n<p>b) For each of the cottage and the house, what is the principal balance owing after 5 years?<\/p>\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p>a) Cottage: The down payment will be $50,000, the monthly payment will be $2110.62 and the total interest will be $183,185.76<\/p>\n<p>House: The down payment will be $88,000, the monthly payment will be $3714.69 and the total interest will be $322,406.93<\/p>\n<p>b)\u00a0 Cottage: After 5 years the balance owing is $384,024.74<\/p>\n<p>House:\u00a0 After 5 years the balance owing is $675,883.55<\/p>\n<\/details>\n<p>&nbsp;<\/p>\n<\/div>\n<\/div>\n<\/div>\n<h1>Key Concepts<\/h1>\n<ul>\n<li>For an Installment Loan:\n<ul>\n<li>to determine the <strong>total installment payments<\/strong>:\n<p style=\"text-align: center;\">Number of Payments x Payment Amount<\/p>\n<\/li>\n<li>to determine the <strong>finance (interest) charge<\/strong>:\n<p style=\"text-align: center;\">\u00a0Total Installment Payments\u00a0 &#8211; Loan Amount<\/p>\n<\/li>\n<li>to determine the <strong>amount financed:<\/strong><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p style=\"text-align: center; padding-left: 40px;\">\u00a0Purchase Price &#8211; Down Payment<\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li>to determine the <strong>total amount paid <\/strong>for the item:<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p style=\"text-align: center; padding-left: 40px;\">Purchase Price + Finance Charge<\/p>\n<p style=\"text-align: center; padding-left: 40px;\">or<\/p>\n<p style=\"text-align: center; padding-left: 40px;\">Total\u00a0 Installment Payments + Down Payment<\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li>to determine the <strong>periodic payment P:<\/strong><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f48374414889122191e897c69588c538_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#80;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#65;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#114;&#125;&#123;&#110;&#125;&#41;&#125;&#123;&#49;&#32;&#45;&#32;&#40;&#49;&#32;&#43;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#114;&#125;&#123;&#110;&#125;&#41;&#94;&#123;&#45;&#110;&#116;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"119\" style=\"vertical-align: -12px;\" \/><\/p>\n<h1><strong>Glossary<\/strong><\/h1>\n<div class=\"textbox shaded\">\n<p><strong>amortization<\/strong><\/p>\n<p>is the process of spreading out a loan into a series of fixed payments.<\/p>\n<p><strong>amount financed<\/strong><\/p>\n<p>is the purchase price of the item less any down payment.<\/p>\n<p><strong>finance charge<\/strong><\/p>\n<p>is the total of the\u00a0 interest charges on a loan.<\/p>\n<p><strong>installment loan<\/strong><\/p>\n<p>is a type of loan that is repaid over time with a set number of scheduled payments (installments). The term of loan may be vary and could be few months or many years.<\/p>\n<p><strong>maturity date<\/strong><\/p>\n<p>is when all principal and\/or interest must be repaid to the lender.<\/p>\n<\/div>\n<h1>9.5 Exercise Set<\/h1>\n<div>\n<ol>\n<li>Bette purchased a new appliance package at a total cost of $7500. She obtained a 3 year loan at an interest rate of\u00a0 5.75%.\u00a0 Her monthly payments will be $227.32 over three years.\n<ol type=\"a\">\n<li>State the amount financed.<\/li>\n<li>Determine the total installment payments.<\/li>\n<li>Determine the finance charge.<\/li>\n<\/ol>\n<\/li>\n<li>Paul purchased a new vehicle at a total cost of $21,300. He obtained a 5 year loan at an interest rate of\u00a0 4.2%.\u00a0 His monthly payments will be $394.20 over five years.\n<ol type=\"a\">\n<li>State the amount financed.<\/li>\n<li>Determine the total installment payments.<\/li>\n<li>Determine the finance charge.<\/li>\n<\/ol>\n<\/li>\n<li>Theresa purchased a home entertainment system at a total cost of $4300. She made a down payment of $1000 and to pay the balance she obtained a 2 year loan at an interest rate of\u00a0 5.5%.\u00a0 Her monthly payments will be $145.52 over two years.\n<ol type=\"a\">\n<li>State the amount financed.<\/li>\n<li>Determine the total installment payments.<\/li>\n<li>Determine the finance charge.<\/li>\n<li>Determine the total amount that Theresa paid for the home entertainment system.<\/li>\n<\/ol>\n<\/li>\n<li>The Johnsons purchased a new vehicle at a total cost of $32,500. They made a down payment of $5000 and to pay the balance they obtained a 4 year loan at an interest rate of\u00a0 3.6%.\u00a0 The monthly payments will be $616.01 over four years.\n<ol type=\"a\">\n<li>State the amount financed.<\/li>\n<li>Determine the total installment payments..<\/li>\n<li>Determine the finance charge.<\/li>\n<li>Determine the total amount that the Johnsons paid for the vehicle.<\/li>\n<\/ol>\n<\/li>\n<li>Determine the monthly (periodic) payment and finance charge for each of the following installment loans.<br \/>\n<table class=\"grid\" style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 20%; text-align: center;\">Annual Interest Rate<\/td>\n<td style=\"width: 20%; text-align: center;\">Number of Years<\/td>\n<td style=\"width: 20%; text-align: center;\">Loan Amount<\/td>\n<td style=\"width: 20%; text-align: center;\">Monthly Payment<\/td>\n<td style=\"width: 20%; text-align: center;\">Finance Charge<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 20%; text-align: center;\">2.8%<\/td>\n<td style=\"width: 20%; text-align: center;\">1<\/td>\n<td style=\"width: 20%; text-align: center;\">$2000<\/td>\n<td style=\"width: 20%; text-align: center;\"><\/td>\n<td style=\"width: 20%; text-align: center;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 20%; text-align: center;\">4%<\/td>\n<td style=\"width: 20%; text-align: center;\">2<\/td>\n<td style=\"width: 20%; text-align: center;\">$4200<\/td>\n<td style=\"width: 20%; text-align: center;\"><\/td>\n<td style=\"width: 20%; text-align: center;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 20%; text-align: center;\">5%<\/td>\n<td style=\"width: 20%; text-align: center;\">3<\/td>\n<td style=\"width: 20%; text-align: center;\">$5200<\/td>\n<td style=\"width: 20%; text-align: center;\"><\/td>\n<td style=\"width: 20%; text-align: center;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 20%; text-align: center;\">4.5%<\/td>\n<td style=\"width: 20%; text-align: center;\">3<\/td>\n<td style=\"width: 20%; text-align: center;\">$8000<\/td>\n<td style=\"width: 20%; text-align: center;\"><\/td>\n<td style=\"width: 20%; text-align: center;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 20%; text-align: center;\">6.5%<\/td>\n<td style=\"width: 20%; text-align: center;\">4<\/td>\n<td style=\"width: 20%; text-align: center;\">$11,000<\/td>\n<td style=\"width: 20%; text-align: center;\"><\/td>\n<td style=\"width: 20%; text-align: center;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<li>A dining room set is purchased for $2300. The purchase is financed\u00a0 with a 2 year loan at an interest rate of 6.4%\n<ol type=\"a\">\n<li>Use the formula to determine the monthly payment<\/li>\n<li>Determine the total installment\u00a0 payments.<\/li>\n<li>Determine the finance charge.<\/li>\n<\/ol>\n<\/li>\n<li>A new vehicle is purchased for $32, 000. The purchase is financed\u00a0 with a 5 year loan at an interest rate of 4.8%.\n<ol type=\"a\">\n<li>Use the formula to determine the monthly payment<\/li>\n<li>Determine the total installment\u00a0 payments.<\/li>\n<li>Determine the finance charge.<\/li>\n<\/ol>\n<\/li>\n<li>The Connors purchase a hot tub for a total price of $8500. They make a downpayment of $2300 and finance the remainder with a 3 year loan at an interest rate of 2.6%.\n<ol type=\"a\">\n<li>Determine the loan amount<\/li>\n<li>Use the formula to determine the monthly payment<\/li>\n<li>Determine the total installment\u00a0 payments.<\/li>\n<li>Determine the finance charge.<\/li>\n<li>How much in total did the Connors actually pay for the hot tub?<\/li>\n<\/ol>\n<\/li>\n<li>The Tanners purchase a small RV for a total price of $48,000. They make a downpayment of $8000 and finance the remainder with a 4 year loan at an interest rate of 3%.\n<ol type=\"a\">\n<li>Determine the loan amount<\/li>\n<li>Use the formula to determine the monthly payment<\/li>\n<li>Determine the total installment\u00a0 payments.<\/li>\n<li>Determine the finance charge.<\/li>\n<li>How much in total did the Tanners actually pay for the RV?<\/li>\n<\/ol>\n<\/li>\n<li>Matt borrows $4000 for 4 years at an interest rate of 5%. He will make 4 annual payments.\n<ol type=\"a\">\n<li>Determine the annual payment and the finance charge.<\/li>\n<li>Complete the following amortization table for the loan.<br \/>\n<table class=\"grid\" style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 20%; text-align: center;\">Year<\/td>\n<td style=\"width: 17.5852%; text-align: center;\">Beginning Balance<\/td>\n<td style=\"width: 19.1478%; text-align: center;\">Interest<\/td>\n<td style=\"width: 23.267%; text-align: center;\">Payment towards the Principal<\/p>\n<p>= Payment &#8211; Interest<\/td>\n<td style=\"width: 20%; text-align: center;\">End Balance<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 20%; text-align: center;\">1<\/td>\n<td style=\"width: 17.5852%; text-align: center;\">$4000<\/td>\n<td style=\"width: 19.1478%; text-align: center;\">$200<\/td>\n<td style=\"width: 23.267%;\"><\/td>\n<td style=\"width: 20%;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 20%; text-align: center;\">2<\/td>\n<td style=\"width: 17.5852%;\"><\/td>\n<td style=\"width: 19.1478%;\"><\/td>\n<td style=\"width: 23.267%;\"><\/td>\n<td style=\"width: 20%;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 20%; text-align: center;\">3<\/td>\n<td style=\"width: 17.5852%;\"><\/td>\n<td style=\"width: 19.1478%;\"><\/td>\n<td style=\"width: 23.267%;\"><\/td>\n<td style=\"width: 20%;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 20%; text-align: center;\">4<\/td>\n<td style=\"width: 17.5852%;\"><\/td>\n<td style=\"width: 19.1478%;\"><\/td>\n<td style=\"width: 23.267%;\"><\/td>\n<td style=\"width: 20%;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<li>Confirm the finance charge by totalling the interest column.<\/li>\n<\/ol>\n<\/li>\n<li>Kate purchases an electric bike for $4800 and she makes a down payment of $2200. She takes out a one year loan at 3.2% to pay the balance owing in monthly payments.\n<ol type=\"a\">\n<li>Determine the amount of the loan<\/li>\n<li>Determine the monthly payment on the loan.<\/li>\n<li>Determine the total installment payments<\/li>\n<li>Determine the finance charge.<\/li>\n<li>Complete the following amortization table for the first four months of the loan. (Hint: When calculating simple interest the time (t) will be 1\/12 of\u00a0 a year).<br \/>\n<table class=\"grid\" style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 20%; text-align: center;\">Year<\/td>\n<td style=\"width: 17.5852%; text-align: center;\">Beginning Balance<\/td>\n<td style=\"width: 19.1478%; text-align: center;\">Interest<\/td>\n<td style=\"width: 23.267%; text-align: center;\">Payment towards the Principal<\/p>\n<p>= Payment &#8211; Interest<\/td>\n<td style=\"width: 20%; text-align: center;\">End Balance<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 20%; text-align: center;\">1<\/td>\n<td style=\"width: 17.5852%; text-align: center;\"><\/td>\n<td style=\"width: 19.1478%; text-align: center;\"><\/td>\n<td style=\"width: 23.267%;\"><\/td>\n<td style=\"width: 20%;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 20%; text-align: center;\">2<\/td>\n<td style=\"width: 17.5852%;\"><\/td>\n<td style=\"width: 19.1478%;\"><\/td>\n<td style=\"width: 23.267%;\"><\/td>\n<td style=\"width: 20%;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 20%; text-align: center;\">3<\/td>\n<td style=\"width: 17.5852%;\"><\/td>\n<td style=\"width: 19.1478%;\"><\/td>\n<td style=\"width: 23.267%;\"><\/td>\n<td style=\"width: 20%;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 20%; text-align: center;\">4<\/td>\n<td style=\"width: 17.5852%;\"><\/td>\n<td style=\"width: 19.1478%;\"><\/td>\n<td style=\"width: 23.267%;\"><\/td>\n<td style=\"width: 20%;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<li>How much did Kate actually pay for the bike?<\/li>\n<\/ol>\n<\/li>\n<li>You purchase a kayak for $4800 and take out a 3 year loan with monthly payments at an annual interest rate of 3.5%. You are pondering whether to put $2000 down or go on a holiday with that $2000.\n<ol type=\"a\">\n<li>Assuming no down payment, determine the monthly payment, total installment payments,\u00a0 and finance charge.<\/li>\n<li>Assuming a down payment of $2000, determine the monthly payment, total installment payments,\u00a0 and finance charge.<\/li>\n<li>What is the difference in finance charges between the two options?<\/li>\n<\/ol>\n<\/li>\n<li>Nick purchases a used motorbike for $12,000 and takes out a 4 year loan with monthly payments at an annual interest rate of 5%.\n<ol type=\"a\">\n<li>Determine the payment, total installment payments, and finance charge with no down payment.<\/li>\n<li>Determine the payment, total installment payments, and finance charge with a down payment of $4000.<\/li>\n<li>What is the difference in finance charges between the two options?<\/li>\n<\/ol>\n<\/li>\n<li>A $350,000 home is purchased with a 20 year mortgage at a fixed interest rate of 3.4% and a down payment of 10%.\n<ol type=\"a\">\n<li>Use an online mortgage calculator to determine the down payment, the monthly payment and the total interest paid.<\/li>\n<li>Determine the total payments for one year.<\/li>\n<li>Generate an amortization schedule and determine how much of the first year&#8217;s payments will go towards principle and how much will go towards interest.<\/li>\n<li>Generate an amortization schedule and determine how much of the final year&#8217;s payments will go towards principle and how much will go towards interest.<\/li>\n<\/ol>\n<\/li>\n<li>A $350,000 home is purchased with a 20 year mortgage at a fixed interest rate of 3.4% and a\u00a0 20% down payment.\n<ol type=\"a\">\n<li>Use an online mortgage calculator to determine the down payment, the monthly payment and the total interest paid<\/li>\n<li>Compare your answers for #14 and #15 Part a). What was the impact on the monthly payment and the total interest charges when the down payment was doubled?<\/li>\n<li>Determine the total payments for one year.<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol type=\"a\">\n<li>A $650,000 home is purchased with a 10% down payment on a 25 year mortgage at a fixed interest rate of 4.2%. \u00a0Use an online mortgage calculator to determine the down payment, the monthly payment and the total interest paid.<\/li>\n<li>\u00a0A $650,000 home is purchased with a 10% down payment on a 25 year mortgage at a fixed interest rate of 2.2%. \u00a0Use an online mortgage calculator to determine the down payment, the monthly payment and the total interest paid<\/li>\n<li>Compare your answers for parts a) and b). How does the lower interest rate impact the total interest paid?<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<h1>Answers<\/h1>\n<ol>\n<li>\n<ol type=\"a\">\n<li>$7500<\/li>\n<li>$8183.52<\/li>\n<li>$683.52<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol type=\"a\">\n<li>$21,300<\/li>\n<li>$23,652<\/li>\n<li>$2352<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol type=\"a\">\n<li>$3300<\/li>\n<li>$3492.48<\/li>\n<li>$192.48<\/li>\n<li>$4492.48<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol type=\"a\">\n<li>$27,500<\/li>\n<li>$29,568.48<\/li>\n<li>$2068.48<\/li>\n<li>$34,568.48<\/li>\n<\/ol>\n<\/li>\n<li>\n<table class=\"grid\" style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 20%; text-align: center;\">Annual Interest Rate<\/td>\n<td style=\"width: 20%; text-align: center;\">Number of Years<\/td>\n<td style=\"width: 20%; text-align: center;\">Loan Amount<\/td>\n<td style=\"width: 20%; text-align: center;\">Monthly Payment<\/td>\n<td style=\"width: 20%; text-align: center;\">Finance Charge<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 20%; text-align: center;\">2.8%<\/td>\n<td style=\"width: 20%; text-align: center;\">1<\/td>\n<td style=\"width: 20%; text-align: center;\">$2000<\/td>\n<td style=\"width: 20%; text-align: center;\"><strong>$169.21<\/strong><\/td>\n<td style=\"width: 20%; text-align: center;\">$30.52<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 20%; text-align: center;\">4%<\/td>\n<td style=\"width: 20%; text-align: center;\">2<\/td>\n<td style=\"width: 20%; text-align: center;\">$4200<\/td>\n<td style=\"width: 20%; text-align: center;\"><strong>$182.38<\/strong><\/td>\n<td style=\"width: 20%; text-align: center;\">$177.12<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 20%; text-align: center;\">5%<\/td>\n<td style=\"width: 20%; text-align: center;\">3<\/td>\n<td style=\"width: 20%; text-align: center;\">$5200<\/td>\n<td style=\"width: 20%; text-align: center;\"><strong>$155.85<\/strong><\/td>\n<td style=\"width: 20%; text-align: center;\">$410.60<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 20%; text-align: center;\">4.5%<\/td>\n<td style=\"width: 20%; text-align: center;\">3<\/td>\n<td style=\"width: 20%; text-align: center;\">$8000<\/td>\n<td style=\"width: 20%; text-align: center;\"><strong>$237.98<\/strong><\/td>\n<td style=\"width: 20%; text-align: center;\">$567.28<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 20%; text-align: center;\">6.5%<\/td>\n<td style=\"width: 20%; text-align: center;\">4<\/td>\n<td style=\"width: 20%; text-align: center;\">$11,000<\/td>\n<td style=\"width: 20%; text-align: center;\"><strong>$260.86<\/strong><\/td>\n<td style=\"width: 20%; text-align: center;\">$1521.28<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<li>\n<ol type=\"a\">\n<li>$102.35<\/li>\n<li>$2456.40<\/li>\n<li>$156.40<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol type=\"a\">\n<li>$600.95<\/li>\n<li>$36,057<\/li>\n<li>$4057<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol type=\"a\">\n<li>$6200<\/li>\n<li>$179.21<\/li>\n<li>$6451.56<\/li>\n<li>$251.56<\/li>\n<li>$8751.56<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol type=\"a\">\n<li>$40,000<\/li>\n<li>$885.37<\/li>\n<li>$42,497.76<\/li>\n<li>$2497.76<\/li>\n<li>$50,497.76<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol type=\"a\">\n<li>Annual Payment = $1128.05. Finance Charge = <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b7345d642662d48e0e7e09e92c830c01_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#49;&#49;&#50;&#56;&#46;&#48;&#53;&#32;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#52;&#41;&#32;&#45;&#32;&#52;&#48;&#48;&#48;&#32;&#61;&#32;&#92;&#36;&#53;&#49;&#50;&#46;&#50;&#48;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"241\" style=\"vertical-align: -5px;\" \/><\/li>\n<li>\n<table class=\"grid\" style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 7.30964%; text-align: center;\">Year<\/td>\n<td style=\"width: 14.9239%; text-align: center;\">Beginning Balance<\/td>\n<td style=\"width: 14.5614%; text-align: center;\">Interest<\/td>\n<td style=\"width: 30.8773%; text-align: center;\">Payment towards the\u00a0 \u00a0 \u00a0 \u00a0Principal (Balance)<\/p>\n<p>= Payment &#8211; Interest<\/td>\n<td style=\"width: 32.3278%; text-align: center;\">End Balance<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 7.30964%; text-align: center;\">1<\/td>\n<td style=\"width: 14.9239%; text-align: center;\">4000<\/td>\n<td style=\"width: 14.5614%; text-align: center;\">200<\/td>\n<td style=\"width: 30.8773%; text-align: center;\">1128.05 &#8211; 200 = 928.05<\/td>\n<td style=\"width: 32.3278%; text-align: center;\">4000 &#8211; 928.05 = 3071.95<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 7.30964%; text-align: center;\">2<\/td>\n<td style=\"width: 14.9239%; text-align: center;\">3071.95<\/td>\n<td style=\"width: 14.5614%; text-align: center;\">153.60<\/td>\n<td style=\"width: 30.8773%; text-align: center;\">1128.05 &#8211; 153.60 = 974.45<\/td>\n<td style=\"width: 32.3278%; text-align: center;\">3071.95 &#8211; 974.45 = 2097.50<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 7.30964%; text-align: center;\">3<\/td>\n<td style=\"width: 14.9239%; text-align: center;\">2097.50<\/td>\n<td style=\"width: 14.5614%; text-align: center;\">104.87<\/td>\n<td style=\"width: 30.8773%; text-align: center;\">1128.05 &#8211; 104.87 = 1023.18<\/td>\n<td style=\"width: 32.3278%; text-align: center;\">2097.50 &#8211; 1023.28 = 1074.32<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 7.30964%; text-align: center;\">4<\/td>\n<td style=\"width: 14.9239%; text-align: center;\">1074.32<\/td>\n<td style=\"width: 14.5614%; text-align: center;\">53.72<\/td>\n<td style=\"width: 30.8773%; text-align: center;\">1128.05 &#8211; 53.72 = 1074.33<\/td>\n<td style=\"width: 32.3278%; text-align: center;\">1074.32 &#8211; 1074.33 = 0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<li>Interest = $512.19 (rounding difference of 1\u00a2)<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol type=\"a\">\n<li>Loan Amount = $2600<\/li>\n<li>Monthly Payment = $220.44<\/li>\n<li>Total Installment payments = $2645.28<\/li>\n<li>Finance Charge =\u00a0 $45.28<\/li>\n<li>\n<table class=\"grid\" style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 7.30964%; text-align: center;\">Year<\/td>\n<td style=\"width: 14.9239%; text-align: center;\">Beginning Balance<\/td>\n<td style=\"width: 14.5614%; text-align: center;\">Interest<\/p>\n<p>(t = 1\/12 year)<\/td>\n<td style=\"width: 30.8773%; text-align: center;\">Payment towards the\u00a0 \u00a0 \u00a0 \u00a0Principal (Balance)<\/p>\n<p>= Payment &#8211; Interest<\/td>\n<td style=\"width: 32.3278%; text-align: center;\">End Balance<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 7.30964%; text-align: center;\">1<\/td>\n<td style=\"width: 14.9239%; text-align: center;\">2600<\/td>\n<td style=\"width: 14.5614%; text-align: center;\">6.93<\/td>\n<td style=\"width: 30.8773%; text-align: center;\">220.44 &#8211; 6.93 = 213.51<\/td>\n<td style=\"width: 32.3278%; text-align: center;\">2600 &#8211; 213.51 = 2386.49<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 7.30964%; text-align: center;\">2<\/td>\n<td style=\"width: 14.9239%; text-align: center;\">2386.49<\/td>\n<td style=\"width: 14.5614%; text-align: center;\">6.36<\/td>\n<td style=\"width: 30.8773%; text-align: center;\">220.44 &#8211; 6.36 = 214.08<\/td>\n<td style=\"width: 32.3278%; text-align: center;\">2386.49 &#8211; 214.08 = 2172.41<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 7.30964%; text-align: center;\">3<\/td>\n<td style=\"width: 14.9239%; text-align: center;\">2172.41<\/td>\n<td style=\"width: 14.5614%; text-align: center;\">5.79<\/td>\n<td style=\"width: 30.8773%; text-align: center;\">220.44 &#8211; 5.79 = 214.65<\/td>\n<td style=\"width: 32.3278%; text-align: center;\">2172.41 &#8211; 214.65 = 1957.76<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 7.30964%; text-align: center;\">4<\/td>\n<td style=\"width: 14.9239%; text-align: center;\">1957.76<\/td>\n<td style=\"width: 14.5614%; text-align: center;\">5.22<\/td>\n<td style=\"width: 30.8773%; text-align: center;\">220.44 &#8211; 5.22 = 215.22<\/td>\n<td style=\"width: 32.3278%; text-align: center;\">1957.76 &#8211; 215.22 = 1742.54<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<li>$4845.28<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol type=\"a\">\n<li>Payment = $140.65;\u00a0 \u00a0Total Installment Payments = $5063.40;\u00a0 Finance Charge = $263.40<\/li>\n<li>Payment = $82.05;\u00a0 \u00a0Total Installment Payments = $2953.65 Finance Charge = $153.65<\/li>\n<li>$109.75 less with a down payment<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol type=\"a\">\n<li>Payment = $276.35;\u00a0 Total\u00a0 Installment Payments = $13264.80;\u00a0 Finance Charge = $1264.80<\/li>\n<li>Payment = $184.23;\u00a0 Total Installment Payments = $8843.04;\u00a0 Finance Charge = $843.04<\/li>\n<li>$421.76 less with a down payment<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol type=\"a\">\n<li>down payment of $35,000; monthly payment of $1810.73;\u00a0 total interest paid\u00a0 $119,574.74<\/li>\n<li>total payments for one year $21,728.76<\/li>\n<li>$10,536.66 towards interest and $11,192.10 towards principal.<\/li>\n<li>$394.95 towards interest and $21,333.81 towards principal.<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol type=\"a\">\n<li>down payment of $70,000; monthly payment of $1609.54;\u00a0 total interest paid\u00a0 $106,288.66<\/li>\n<li>With the downpayment being doubled, the monthly payment was reduced by close to $200 and the total interest paid was reduced by more than $13,000.<\/li>\n<li>$19,314.48<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol type=\"a\">\n<li>down payment of $65,000; monthly payment of $3152.81;\u00a0 total interest paid\u00a0 $360,843.77<\/li>\n<li>down payment of $65,000; monthly payment of $2536.90;\u00a0 total interest paid\u00a0 $176,070.84<\/li>\n<li>the total interest is almost $200,000 less!<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<\/div>\n","protected":false},"author":125,"menu_order":5,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1836","chapter","type-chapter","status-publish","hentry"],"part":1718,"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapters\/1836","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/wp\/v2\/users\/125"}],"version-history":[{"count":3,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapters\/1836\/revisions"}],"predecessor-version":[{"id":2135,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapters\/1836\/revisions\/2135"}],"part":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/parts\/1718"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapters\/1836\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/wp\/v2\/media?parent=1836"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapter-type?post=1836"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/wp\/v2\/contributor?post=1836"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/wp\/v2\/license?post=1836"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}